Post on 12-Jan-2016
description
ETH Zurich – Distributed Computing – www.disco.ethz.ch
Silvio Frischknecht, Barbara Keller, Roger Wattenhofer
Convergence in (Social) Influence Networks
Simple World
2 Opinions:
Opinion changes: Whatever the majority of my friends think
b
b
b
b
b
What Can Happen?
and/or
Goles and Olivios 1980
Easy Lower Bound: Ω(n)
Easy Lower Bound: Ω(n)
Easy Lower Bound: Ω(n)
Easy Lower Bound: Ω(n)
Easy Lower Bound: Ω(n)
Upper Bound:
v
)( 2nO
v
Upper Bound: )( 2nO
v
Upper Bound: )( 2nO
Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion
v
Upper Bound: )( 2nO
Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion
v
t t+1 t+2
vg
b
g: Nr. of good edges b: Nr. of bad edges
case g > b
Upper Bound: )( 2nO
Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion
v
t t+1 t+2
vg
b
g: Nr. of good edges b: Nr. of bad edges
case g > b
Upper Bound: )( 2nO
Good edge: Friend takes advised opinion on next dayBad edge: Friend does not take the proposed opinion
v
t t+1 t+2
vg
b
g: Nr. of good edges b: Nr. of bad edges
case g > b
Upper Bound: )( 2nO
v
t t+1 t+2
vg
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
v
t t+1 t+2
vg
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
v
t t+1 t+2
vg
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
v
t t+1 t+2
vg
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
b
g
Tight Bound?
Lower bound Upper bound vs.
2nn
Let`s Vote
vs. 2nn
n
n2
2
log
Simpler Example: nn
Simpler Example: nn
A Transistor
A Transistor
B
C
EB
C
E
BC
E
E
CB
BC
E
BE
C
B BC
E E
C
BC
E
BBBE E E
C C C
BE
CBB
CC
EE
Other Results
Iterative model: Adversary picks nodes instead of synchronous rounds:
1 Step = 1 node change its opinion
Convergence Time: θ(n²)
Iterative Model
Benevolent algorithm: θ(n)
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