spanning tree method for link state aggregation in large communication networks whay choiu lee

Spanning Tree Method for Link State Aggregation in Large Communication

Networks

Whay Choiu Lee

Overview

IntroductionExisting methods for link state aggregation

symmetric-pointfull-meshstar

Spanning Tree Methodintuitionproperties of spanning treehow does it work

DiscussionSummary

Introduction

Why is the link state aggregation needed? Complexity of link state updates( O(n2) ). Security.

Criteria of desirable link state aggregation: Adequately represents the original network. Significantly compresses the original network.

Introduction

Common solution for complexity reduction Hierarchical structure.

Boarder nodes Logical links

Subnetwork Topology

A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)

(bandwidth, delay)

non-additive, additive

Existing methods for link state aggregation

Symmetric-point

Pro:greatest reduction.O(1).

Con:does not adequately reflect

any asymmetric topology.does not capture any multiple

connectivity.

(2,30)

A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)


Full-Mesh

Pro:adequate

representation.flexibility.

A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)A B

CD(6,24)

(7,17)

(6,21)

(4,27)

(4,13)

Con:link state explosion.O(n2).

(4,18)


Star

Pro:limited flexibility.O(n).

A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)A B

CD

Con:does not capture any multiple

connectivity.

(1,15)

Spanning tree method

Idea: Represent the original subnetwork by full-mesh topology

consisting of predetermined subset of the nodes. Encode the link state information associated with the full-

mesh representation. Advantages:

O(n). Link state of nodes not on spanning tree may be derived or

estimated. Multiple connectivity.


Properties of spanning tree: Tree: connecting set of nodes with no loop. G(N, N-1). Unique path connecting each pair of nodes. Maximum spanning tree vs. minimum spanning tree.

Maximum weight spanning tree:d <= min(a,b,c)

Minimum weight spanning tree:d >= max(a,b,c)

A B

CD

b a d c

Spanning Tree


1. Determine maximum bandwidth path for each pair of border nodes.

2. Create logical link between each pair of border nodes to form a full-mesh, and assign it the (bandwidth, delay) of maximum bandwidth path.

3. Generate one maximum weight spanning tree based on bandwidth, and another based on delay.

Constructing Maximum-Bandwidth Full-Mesh Representation

shortest-widest routing algorithm

A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)



A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)

D-A (7,17)



A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)

D-A (7,17)D-B (4,27)



A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)

D-A (7,17)D-B (4,27)D-C (6, 21)



A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)

D-A (7,17)D-B (4,27)D-C (6, 21)

C-A (6, 24)



A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)

D-A (7,17)D-B (4,27)D-C (6, 21)

C-A (6, 24)C-B (4, 18)



A B

CD

(7,10)

(4,8)

(7,7)

(5,5)

(9,8)

(3,4)

(4,7)

(6,6)

(2,3)

(10,5)

D-A (7,17)D-B (4,27)D-C (6, 21)

C-A (6, 24)C-B (4, 18)

B-A (4,13)

Maximum-Bandwidth Full-Mesh Representation

D-A (7,17)D-B (4,27)D-C (6, 21)

C-A (6, 24)C-B (4, 18)

B-A (4,13)A B

CD

(6,24)

(7,17)

(6,21)

(4,27) (4,18

)

(4,13)

Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm

Initialize tree T = Ø. Scan links in descending order of

weight. If adding edge E to tree T create a

loop Edge is excluded.

Otherwise, edge is included in Tree T.


D-A (7,17)D-B (4,27)D-C (6, 21)

C-A (6, 24)C-B (4, 18)

B-A (4,13)A B

CD

(6,24)

(7,17)

(6,21)

(4,27) (4,18

)

(4,13)


A B

CD

(6,24)

(7,17)

(6,21)

(4,27) (4,18

)

(4,13)

D-A (7,17)D-B (4,27)D-C (6, 21)

C-A (6, 24)C-B (4, 18)

B-A (4,13)

Maximum-Weight Spanning Tree for Bandwidth

A B

CD

6

7

6

4 4

4

Maximum-Weight Spanning Tree for Delay

A B

CD

24

17

21

27 18

13

Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search

A B

CD

6

7

6

4 4

4

Root A


A B

CD

6

7

6

4 4

4

Root A: E(AD)


A B

CD

6

7

6

4 4

4

Root A: E(AD), E(AC)


A B

CD

6

7

6

4 4

4 = min(6,4)

Root A: E(AD), E(AC), E(CB)

Decoded Full-Mesh for Bandwidth

A B

CD

6

7

6

4 4

4

Decoded Full-Mesh for Delay

A B

CD

24

21

21

27 21

21

Discussion: Full-Mesh Topology Comparison

A B

CD

(6, 24)

(7,21)

(6,21)

(4,27) (4,21

)

(4,21)

(4,18) c

A B

CD

(6,24) b

(7,17) a

(6,21)

(4,27) d

(4,13)

Maximum-Bandwidth Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

Perfect encoding for bandwidth: d = min(a,b,c)Upper-bound for delay: d <= min(a,b,c)

Full-Mesh Topology Comparison

A B

CD

(6, 24)

(7,21)

(6,21)

(4,27) (4,21

)

(4,21)

(4,18) c

A B

CD

(6,24) b

(7,17) a

(6,21)

(4,27) d

(4,13)

Maximum-Bandwidth Full-Mesh Decoded Maximum-Bandwidth Full-Meshmaximum spanning tree: d <= min(a,b,c).

Perfect encoding for bandwidth: d = min(a,b,c)maximum weight full-mesh: d >= min(a,b,c).

Upper-bound for delay: d <= min(a,b,c)

Discussion: Full-Mesh Topology Problem

A B

CD

(6, 24)

(7,21)

(6,21)

(4,27) (4,21

)

(4,21)

A B

CD

(2,16)

(7,17)

(3,15)

(2,18) (2,3)

(4,13)

Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

Discussion: Full-Mesh Topology Problem

A B

CD

(6, 24)

(7,21)

(6,21)

(4,27) (4,21

)

(4,21)

A B

CD

(2,16)

(7,17)

(3,15)

(2,18) (2,3)

(4,13)

Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

Call: C-D (3, 15)

summary

Spanning tree method Full-mesh topology generation. Spanning tree construction. Topology recovery from spanning tree.

Discussion Perfect encoding vs. upper-bound. Conservative.

questions

spanning tree method for link state aggregation in large communication networks whay choiu lee

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