1

Efficient prefix updates for IP router using lexicographic ordering and updateable

address set

Authors: Sieteng Soh, Lely Hiryanto and Surech

Publisher: IEEE Transactions on Computer, 2008

Present: Chen-Yu Lin

Date: Feb,25, 2009

Notations and background

Notations :• A routing table T contains a list of pairs T = (p, h).

• Assume that T contains a pair (ε,hε) (the default next-hop interface). A table T is sorted in decreasing lexicographic order. <T1 ,T2 ,…,Tn >.

• Ti precedes Tj if and only if i < j and pj is lexicographically in lower order than pi .

• pi > pj , if• 1. pj = prefix(pi)

• 2. for some value of 0 < k ≤ min(|pi|,| pj |), the first k-1 bits of the two prefix agree, but the kth bit of pi (=1) is larger than the kth bit of pj(=0).

2

Notations and background

Given a routing table T, construct a next-hop array (NHA) of size 2w *1.

3

Note:NHA could solve the IP lookup problem in 1 MA.

Notations and background

The FEC (full expansion/compression) techniques• [2] propose an FEC structure that is comprised of a 2D NHA (called table F).• A 32-bit address X=a.b.c.d is split into Xr

0 = a.b and Xcr = c.d

• In this scheme, the lookup for X is in 3 MAs.• However, a prefix update on this scheme is difficult.

4

Notations and background

The CNHA/CWA (Compressed next hop array/code word array) scheme• This scheme split each IP address X=a.b.c.d into a segment a.b and an offset c.d • [5] proposed using a ST(Segment Table) with 216 entries, each of which stores

either a next hop or a pointer to an associated NHA (with 216 entries contains next hop).

• [5] took advantage of the distribution of the prefixes within a segment to reduce the size of its NHA so that the size depends on the length of the longest prefix in the segment 16 < l ≤ 32.

• Each entry in ST contains a 28-bit pointer or a 28-bit next hop and a 4-bit offset length k.

5

offset

Goals of paper

In this paper, we propose a faster algorithm for constructing RLE sequences and an efficient unification technique for reducing the FEC construction time.

In this paper, we propose the use of lexicographically decreasing ordered prefixes to construct the CNHA and CWA structure for a given segment in O(m) time. In addition, using the updateable address set concept, we propose a technique to enable the CNHA/CWA scheme for online prefixes updates.

6

Updates using Lexicographic ordered prefix

7

Aggregated IP addresses of a prefix pq

Lowest address in Aq

Highest address in Aq

Some properties of lexicographic ordered prefixes.

Property 1. Property 2. Property 3.

A sequence of prefixes sorted in decreasing lexicographic order

Updates using Lexicographic ordered prefix

Ti = (pi, hi). A segment q, denoted by ST[q] or STq , contains:

• The length of longest prefixes in ST[q] , l = max(lj).

• A list of triples STjq = (subprefix spj, prefix length lj ≤ 32, next hop hj).

Each Ti with |pi|≥ 16• Represented in a segment ST[q = (pi )0

16 ] by a triple

Each Ti with |pi|< 16• Needs to be expanded into a set • Represented as a triple (0.0, | pi |, hj) in 216-|p

i|

8

Updates using Lexicographic ordered prefix

Some examples: • T = 200.27.240/20/B

• Represented in segment ST[200.27] as a triple (240.0, 20, B).• T = 200.27/16/C

• Represented in segment ST[200.27] as a triple (0.0, 16, C).• T = 200.24/14/C

• Represented in 4 segment ST[200.24], ST[200.25], ST[200.26], ST[200.27] as a triple (0.0, 14, C).

Letbe a sequence of triples (ssi, sei, hi)

9

Starting address Ending

address

Updates using Lexicographic ordered prefix

10

Updates using Lexicographic ordered prefix

Efficient RLE sequence generation• For each segment ST[q], we generate a set of sequences RLE[q] ; thus , for an ST,

we obtain a table RLE.• Each RLE[q] contains a sequence of RLEi

q = <starti, endi, hi>.

• 0 ≤ starti ≤ endi ≤ 216 -1.

• Note that we use this RLE table to construct the FEC and CNHA/CWA structures. As an example, consider ST[200.27].

11

111

Updates using Lexicographic ordered prefix

12

111

111

update

Updates using Lexicographic ordered prefix

Improved technique for FEC table construction.• Convert table RLE into the FEC structure.• Note that table RLE is equivalent to row R of the FEC structure, hence, its

conversion is straightforward.• The row compression steps for FEC can be directly processed by sequentially

deleting any duplicate RLEq and adjusting its corresponding pointer.

13

Updates using Lexicographic ordered prefix

[2] used a function so that each of the non-duplicate RLE sequences contains the same number of RLEs.

In this unification step, an RLEiq = <starti, endi, hi> may be expanded into

14

Updates using Lexicographic ordered prefix

15

Updates using Lexicographic ordered prefix

Improved technique for the CNHA/CWA construction.• First construct table ST. Let 0 ≤ l ≤ 32 be the length of the longest prefix in ST[q].• For l ≤ 16 : S[q] = h• For l > 16 : S[q].offset_length = l – 16 . We use the function below to construct a

CNHAq and CWAq from RLE[q].

16

Updates using Lexicographic ordered prefix

Example : consider RLE[200.27] in previous figure.

17

|RLE| = 6l = 20

For i = 0 :

CNHA[0] = Cstart0 = 0a0 = 0s0 = 0w0 = 0CWA[0].mapw = 1000000000000000CWA[1].base = 1

For i = 1 :

CNHA[1] = Astart1 = 16384a1 = 4s1 = 0w1 = 4CWA[0].mapw = 1000100000000000CWA[1].base = 2

Updates using Lexicographic ordered prefix

18

Updates using Lexicographic ordered prefix

19

Experimental results

Databases for test data

FEC table construction time

20

Experimental results Online prefix update time on DFEC

The CNHA/CWA construction time

21

Experimental results Online prefix update time for the CNHA/CWA scheme

22

23