lidongwuutdallasedu

Small Sensor Big Data

Ding-Zhu DuUniversity of Texas at Dallas

lidongwuutdallasedu

Small Sensor and Big Data

Lidong WuUniversity of Texas at Dallas

Sensor

Drowning in Vast Amount of DataDigitized World

BigData

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Have you watched movie Twister

sensorBucket ofsensors

tornado

lidongwuutdallasedu

Small Sensor and Big Data

Lidong WuUniversity of Texas at Dallas

Sensor

Drowning in Vast Amount of DataDigitized World

BigData

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Have you watched movie Twister

sensorBucket ofsensors

tornado

Sensor

Drowning in Vast Amount of DataDigitized World

BigData

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Have you watched movie Twister

sensorBucket ofsensors

tornado

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Have you watched movie Twister

sensorBucket ofsensors

tornado

Outline

I Data Collection in Sensor System

II Data Analysis on Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

Have you watched movie Twister

sensorBucket ofsensors

tornado

Have you watched movie Twister

sensorBucket ofsensors

tornado

Where are all the sensors

Smartphone with a dozen of sensors

Where are all the sensors

Wearable devices - Google Glass Applersquos iWatch

Buildings

Where are all the sensors

Transportation systems etc

Where are all the sensors

Sensor Web

Large of simple sensors Usually deployed randomly Multi-hop wireless link Distributed routing No infrastructure Collect data and send it to base station

Applications of Senor Web

observerAn example of sensor web

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Where are all the sensors

Wearable devices - Google Glass Applersquos iWatch

Buildings

Where are all the sensors

Transportation systems etc

Where are all the sensors

Sensor Web

Large of simple sensors Usually deployed randomly Multi-hop wireless link Distributed routing No infrastructure Collect data and send it to base station

Applications of Senor Web

observerAn example of sensor web

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Buildings

Where are all the sensors

Transportation systems etc

Where are all the sensors

Sensor Web

Large of simple sensors Usually deployed randomly Multi-hop wireless link Distributed routing No infrastructure Collect data and send it to base station

Applications of Senor Web

observerAn example of sensor web

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Transportation systems etc

Where are all the sensors

Sensor Web

Large of simple sensors Usually deployed randomly Multi-hop wireless link Distributed routing No infrastructure Collect data and send it to base station

Applications of Senor Web

observerAn example of sensor web

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Sensor Web

Large of simple sensors Usually deployed randomly Multi-hop wireless link Distributed routing No infrastructure Collect data and send it to base station

Applications of Senor Web

observerAn example of sensor web

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Applications of Senor Web

observerAn example of sensor web

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

observerAn example of sensor web

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Whatrsquos Sensor

Small size Large number Tether- lessBUThellip

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Whatrsquos limiting the task

Energy Sense Communication scale

CPU

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Challenge

Target is Covered

Sensor system is Connected

Coverage amp Connectivity

Golden Rule then we say

System is alive

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

sensor

target

communication radius

sensing radius

Rc

Rs

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Coverage amp Connectivity

Communication Range

Sensing Range

d le Rs

d le Rc

sensor

target

communication radius

sensing radius

Rc

Rs

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Min-Connected Sensor Cover Problem

Figure Min-CSC Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

[Resource Saving]

communicationnetwork

sensing disks

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Previous Work for PTAS

Itrsquos NP-hard

Ο(r ln n) ndash approximation given by Gupta Das and Gu [MobiHocrsquo03 2003] where n is the number of sensors and r is the link radius of the sensor network

Min-Connected Sensor Cover Problem

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Main Results

Random algorithm

Ο(log3n log log n)-approximation n is the

number of sensors

Partition algorithm

Ο(r)-approximation r is the link radius of the

network

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

With a random algorithm which with probability 1- ɛ produces an Ο(log3n log log n) - approximation

1

Algorithm 1

Group

Steiner Tree

2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Sensor Cover Problem

A uniform set of sensors and a target area

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target area and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

How to map to GST

Min-Connected Target Coverage Problem

A uniform set of sensors and a target POINTS

Find a minimum of sensors

to meet two requirements

[Coverage] cover the target POINTS and

[Connectivity] form a connected communication network

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

A graph G = (V E) with positive edge weight c for every edge e isin E

A specified vertex r

k subsets (or groups) of vertices G1Gk Gi sube V

Find a minimum total weight tree T contains at least one vertex in each Gi

Group Steiner Tree

Figure GST ProblemThis tree has minimum weight

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

Choose at least one sensor from each group

Coverage

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Consider communication network

Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

b3

b1

b2

b6

b5

b4

S1S2

S3S4

b7

Find a group Steiner tree in communication network

Min-Coverage amp Connectivity

b2 b6b3 b4b1 b5 b7

S1 S2

S1 S3

S1 S2 S3

S2 S3

S2 S4

S3 S4

Gi contains all sensors covering bi

S2 S3 S4

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

1 2Min-CSC Min-CTC GST

Garg Konjevod and Ravi [SODA 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n log log n log k) from optimal

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

What Is Link Radius

3 example In this onintersecti sensing

nonempty having sensors twoof distancefor boundupper least theis radiuslink

r

r

Communication disk

Sensing disk

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Connected

Sensor Cover with Target

Area

Connected

Sensor Cover

with Target Points

Connect output of Min-TC into Min-CTC It can be done in Ο(r) - approximation

1

Algorithm 2

2Min-CSC Min-CTC Min-TC

Refer to my paper [INFOCOM 2013rsquo]

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

There exists a polynomial-time (1 + ε)- approximation for MIN-TC

Green is an opt (TC)

Orange is an approx (TC)

lt (1+ε) opt (TC) lt (1+ε) opt (CTC)

Step 2 Target Coverage

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Byrka et al [6] showed there exists a polynomial-time139-approximation of for Network Steiner Minimum Tree

Green is an opt (Network ST)

Red is an approx (TC)

Step 2 Network Steiner Tree

Let Sprime sube S be a (1 + ε)-approximation for MIN-TC Assign

weight one to every edge of G Interconnect sensors in Sprime to

compute a Steiner tree T as network Steiner minimum tree

All sensors on the tree form an approxfor min CTC

nodes approx for min CTC= edges +1 approx for Network STlt 139 opt (Network ST) +1lt 139 opt (CTC) + 1

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Step 2 Network Steiner Tree

Green is an opt (CTC)

Yellow is an approx (TC)

Each orange line has distance lt r

opt (Network ST)

lt opt (CTC) -1 + r = opt (CTC) O(r)

Note lt (1+ε) opt (CTC)

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Future Works

Ο(log3n log log n)

n is the number of sensors

1 Unknown Relationship

2 Constant-appro for Min-CSC

Ο(r)

r is the link radius

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

ldquoConstant-Approximations for Target Coverage Problem in Wireless Sensor Networksrdquo INFOCOM2012 (with Weili Wu et al)

ldquoApproximations for Minimum Connected Sensor Coverrdquo INFOCOM2013 (with Weili Wu et al)

ldquoPTAS for Routing-Cost Constrained Minimum Connected Dominating Sets helliprdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

ldquoAn Approximation Algorithm for Client Assignment helliprdquo INFOCOM2014 (with Weili Wu et al)

What I have donePublications on Optimization

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

CCF 0829993 Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments

CNS 1018320 Undersea Sensor Networks for Intrusion Detection Foundations and Practice

CNS 0831579 Throughput Optimization in Wireless Mesh Sensor Networks

NSF SupportAbove work was supported under the following grants

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

ldquoThe small world networkis a type of mathematical graph in which most nodes are not neighbors of one another but most nodes can be reached from every other by a small number of hops or stepsrdquo

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Social Network A New Frontier

Most of social networks are small world networks with large size

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

The experimentbull Random people from Nebraska

were to send a letter (via intermediaries) to a stock broker in Boston

bull Could only send to someone with whom they know

Among the letters that found the target the average number

of steps was six

Milgram (1967)

Stanley Milgram (1933-1984)

Itrsquos a small world after all

Six Steps of Separation

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Family Friend

Family

Friend

Interviewer

Friend

Supervisor

Friend

Roommate

Friend

Six Steps of Separation

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Social Networks in Life

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Increasing Popularity

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

The trend effect that Kate Duchess of Cambridge has on others from cosmetic surgery for brides to sales of coral-colored jeansrdquo

ldquoKate Middleton Effect

Usage Example 1

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

According to Newsweek The Kate Effect may be worth pound1 billion to the UK fashion industry

Tony DiMasso L K Bennettrsquos US president stated in 2012 when she does wear something it always seems to go on a waiting list

Hike in Sales of Special Products

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

bull Influential Person

bull Kate is one of the persons that have many friends in this social network

How to Find Kate

For more kates itrsquos not as easy as you might think

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Challenge an overall consideration of influence

bullFor example Positive Influence Influence Maximization

Influence Minimization

Find More Kate

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

bullGiven k

bullFind k seeds (Kates) to maximize the number of influenced persons

Influence Maximization

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Influence Maximization

51

Influence Maximization

of influenced nodes is 6

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Influence Maximization

52

of influenced nodes is 6 of influenced nodes is 16

Influence Maximization

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

ldquoBetter Approximations for Influence Maximization in Online Social Networksrdquo Journal of Combinatorial Optimization 2013 (with Weili Wu et al)

Ongoing ResearchInitial Result

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

Search Cheap Ticket

Usage Example 2

There are about 28537 commercial flights in the sky in the US on any given day

bull It is a shortest path problem in a big data network

How to find cheap ticket

bull It is a shortest path problem in a big data network

How to find cheap ticket

Cheap ticket-Graph

AA123

AA456

AA789Dallas Chicago

Cheap ticket-Graph

Dallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

Each city has a set of startpoints and a set of endpointsThey are connected into a bipartite graph based on certain rules

Cheap Ticket-GraphDallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

transition

thedo cost to a ngrepresenti weight a have also

may city each at graph bipartite theof edgeEach

Cheap Ticket-Graph

Dallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

pathshortest node-to-Node

If searching area is larger then searching needs

more time but ticket price may be cheaper

Hard to do it in real-time

Better software is needed

Time VS Price

Challenge

Ongoing ResearchInitial Result

ldquoSocial Network Path Analysis Based on HBaserdquo CSoNet 2013 (with Weili Wu et al)

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 62
• Slide 65
• Slide 66
• Slide 68
• Slide 69

Cheap ticket-Graph

Dallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

Each city has a set of startpoints and a set of endpointsThey are connected into a bipartite graph based on certain rules

Cheap Ticket-GraphDallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

transition

thedo cost to a ngrepresenti weight a have also

may city each at graph bipartite theof edgeEach

Cheap Ticket-Graph

Dallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

pathshortest node-to-Node

If searching area is larger then searching needs

more time but ticket price may be cheaper

Hard to do it in real-time

Better software is needed

Time VS Price

Challenge

Ongoing ResearchInitial Result

ldquoSocial Network Path Analysis Based on HBaserdquo CSoNet 2013 (with Weili Wu et al)

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 62
• Slide 65
• Slide 66
• Slide 68
• Slide 69

Cheap Ticket-GraphDallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

transition

thedo cost to a ngrepresenti weight a have also

may city each at graph bipartite theof edgeEach

Cheap Ticket-Graph

Dallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

pathshortest node-to-Node

If searching area is larger then searching needs

more time but ticket price may be cheaper

Hard to do it in real-time

Better software is needed

Time VS Price

Challenge

Ongoing ResearchInitial Result

ldquoSocial Network Path Analysis Based on HBaserdquo CSoNet 2013 (with Weili Wu et al)

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 62
• Slide 65
• Slide 66
• Slide 68
• Slide 69

Cheap Ticket-Graph

Dallas

8am

9am

1pm 1pm

9am

3pm 3pm

8am

pathshortest node-to-Node

If searching area is larger then searching needs

more time but ticket price may be cheaper

Hard to do it in real-time

Better software is needed

Time VS Price

Challenge

Ongoing ResearchInitial Result

ldquoSocial Network Path Analysis Based on HBaserdquo CSoNet 2013 (with Weili Wu et al)

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 62
• Slide 65
• Slide 66
• Slide 68
• Slide 69

If searching area is larger then searching needs

more time but ticket price may be cheaper

Hard to do it in real-time

Better software is needed

Time VS Price

Challenge

Ongoing ResearchInitial Result

ldquoSocial Network Path Analysis Based on HBaserdquo CSoNet 2013 (with Weili Wu et al)

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 62
• Slide 65
• Slide 66
• Slide 68
• Slide 69

Ongoing ResearchInitial Result

ldquoSocial Network Path Analysis Based on HBaserdquo CSoNet 2013 (with Weili Wu et al)

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 62
• Slide 65
• Slide 66
• Slide 68
• Slide 69

Outline

I Data Collection in Sensor System

II Data Analysis On Social Networks Kate Middleton Effect Search cheap ticket

III Final Remarks

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Slide 43
• Slide 44
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 62
• Slide 65
• Slide 66
• Slide 68
• Slide 69

SSS (Sensor and Sensing Systems) sensor networks with application in industrial engineering

Big Data Program Critical Techniques and Technologies for Advancing Big Data Science amp Engineering

NSF Grant PossibilitiesIn SSS Program amp Big Data Program

Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

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Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF

REU 0851848 Verification and Validation for Software Safety (co-PI Weili Wu)

NSF Grant PossibilitiesIn REU Program

THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

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THANK YOU

in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

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in nodes fromn informatio of

number half aleast at receives nodesother ofeach

such that (Kates) nodes seed of subset aidentify

want to wenetwokion communicat ain Suppose

D

D

Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

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Theorem

problemset dominating

influence positive for theion approximat-)1(

time-polynomial a exists therenetworks socialIn

O

Mathematical Model (II)

Given a graph find a positive influence dominating set with minimum cardinality

Positive Influence Dominating Set Problem

Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

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Mathematical Model (I)

in nodes 2)deg(least at by

dominated is nodeevery ifset dominating

influence positive a called is eFurthermor

oadjacent tor in either is

nodeevery ifset dominating a is subset nodeA

)(graph aConsider

Dv

DVu

D

DD

D

EVG

Dominating set

Positive influence dominating set

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