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Spanning Tree Method for Link State Aggregation in Large Communication Networks

This overview discusses the need for link state aggregation in large networks, exploring existing methods like symmetric-point, full-mesh, and star. The Spanning Tree Method is introduced, outlining its properties, advantages, and how it works. The method involves representing the original network with a full-mesh topology based on predetermined border nodes and encoding link state information for compression. It also explains the process of constructing maximum-bandwidth full-mesh representations using the greedy algorithm. This comprehensive guide provides insights into efficiently managing link state updates in complex communication networks.

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Spanning Tree Method for Link State Aggregation in Large Communication Networks

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  1. Spanning Tree Method for Link State Aggregation in Large Communication Networks Whay Choiu Lee

  2. Overview Introduction Existing methods for link state aggregation symmetric-point full-mesh star Spanning Tree Method intuition properties of spanning tree how does it work Discussion Summary

  3. 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.

  4. Introduction • Common solution for complexity reduction • Hierarchical structure. • Boarder nodes • Logical links

  5. Subnetwork Topology B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C (5,5) (bandwidth, delay) non-additive, additive

  6. A B (4,8) (10,5) (7,10) (4,7) (2,30) (2,3) (7,7) (9,8) (6,6) (3,4) D C (5,5) 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.

  7. A B (4,8) (10,5) (7,10) (4,7) (2,3) (7,7) (9,8) (6,6) (3,4) D C (5,5) Existing methods for link state aggregation • Full-Mesh A B (4,13) (7,17) (4,18) (4,27) (6,24) (6,21) D C Pro: adequate representation. flexibility. Con: link state explosion. O(n2).

  8. A B (4,8) (10,5) (7,10) (4,7) (2,3) (7,7) (9,8) (6,6) (3,4) D C (5,5) Existing methods for link state aggregation • Star A B (1,15) D C Pro: limited flexibility. O(n). Con: does not capture any multiple connectivity.

  9. 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.

  10. Spanning tree method • 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. A B Maximum weight spanning tree: d <= min(a,b,c) Minimum weight spanning tree: d >= max(a,b,c) a c d b D C Spanning Tree

  11. Spanning tree method • 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.

  12. Constructing Maximum-Bandwidth Full-Mesh Representationshortest-widest routing algorithm B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C (5,5)

  13. Constructing Maximum-Bandwidth Full-Mesh Representationshortest-widest routing algorithm D-A (7,17) B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C (5,5)

  14. Constructing Maximum-Bandwidth Full-Mesh Representationshortest-widest routing algorithm D-A (7,17) D-B (4,27) B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C (5,5)

  15. Constructing Maximum-Bandwidth Full-Mesh Representationshortest-widest routing algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C (5,5)

  16. Constructing Maximum-Bandwidth Full-Mesh Representationshortest-widest routing algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C C-A (6, 24) (5,5)

  17. Constructing Maximum-Bandwidth Full-Mesh Representationshortest-widest routing algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C C-A (6, 24) C-B (4, 18) (5,5)

  18. Constructing Maximum-Bandwidth Full-Mesh Representationshortest-widest routing algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B-A (4,13) B A (4,8) (10,5) (7,10) (4,7) (7,7) (2,3) (9,8) (6,6) D (3,4) C C-A (6, 24) C-B (4, 18) (5,5)

  19. B A (4,13) (7,17) (4,27) (4,18) (6,24) (6,21) D C Maximum-Bandwidth Full-Mesh Representation D-A (7,17) D-B (4,27) D-C (6, 21) B-A (4,13) C-A (6, 24) C-B (4, 18)

  20. 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.

  21. B A (4,13) (7,17) (4,27) (4,18) (6,24) (6,21) D C Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B-A (4,13) C-A (6, 24) C-B (4, 18)

  22. Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B-A (4,13) B A (4,13) (7,17) (4,27) (4,18) (6,24) (6,21) D C C-A (6, 24) C-B (4, 18)

  23. Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B-A (4,13) B A (4,13) (7,17) (4,27) (4,18) (6,24) (6,21) D C C-A (6, 24) C-B (4, 18)

  24. Deriving Maximum-Weight Spanning Tree for Bandwidthgreedy algorithm D-A (7,17) D-B (4,27) D-C (6, 21) B-A (4,13) B A (4,13) (7,17) (4,27) (4,18) (6,24) (6,21) D C C-A (6, 24) C-B (4, 18)

  25. Maximum-Weight Spanning Tree for Bandwidth B A 4 7 4 4 6 6 D C

  26. Maximum-Weight Spanning Tree for Delay B A 13 17 27 18 24 21 D C

  27. Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search Root A B A 4 7 4 4 6 6 D C

  28. Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search Root A: E(AD) B A 4 7 4 4 6 6 D C

  29. Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search Root A: E(AD), E(AC) B A 4 7 4 4 6 6 D C

  30. Decoding Maximum-Weight Spanning Tree for Bandwidthdepth-first-search Root A: E(AD), E(AC), E(CB) B A 4 = min(6,4) 7 4 4 6 6 D C

  31. Decoded Full-Mesh for Bandwidth B A 4 7 4 4 6 6 D C

  32. Decoded Full-Mesh for Delay B A 21 21 27 21 24 21 D C

  33. Discussion: Full-Mesh Topology Comparison B A A B (4,21) (4,13) (7,21) (4,27) (7,17) a (4,21) (4,27) d (6, 24) (4,18) c (6,24) b (6,21) D C (6,21) D C 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)

  34. Full-Mesh Topology Comparison B A A B (4,21) (4,13) (7,21) (4,27) (7,17) a (4,21) (4,27) d (6, 24) (4,18) c (6,24) b (6,21) D C (6,21) D C Maximum-Bandwidth Full-Mesh Decoded Maximum-Bandwidth Full-Mesh maximum 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)

  35. Discussion: Full-Mesh Topology Problem B A A B (4,21) (4,13) (7,21) (4,27) (7,17) (4,21) (2,18) (6, 24) (2,3) (2,16) (6,21) D C (3,15) D C Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

  36. Discussion: Full-Mesh Topology Problem Call: C-D (3, 15) B A A B (4,21) (4,13) (7,21) (4,27) (7,17) (4,21) (2,18) (6, 24) (2,3) (2,16) (6,21) D C (3,15) D C Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

  37. Discussion: Full-Mesh Topology Problem Call: C-D (3, 15) B A A B (4,21) (4,13) (7,21) (4,27) (7,17) (4,21) (2,18) (6, 24) (2,3) (2,16) (6,21) D C (3,15) D C Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

  38. Discussion: Full-Mesh Topology Problem Call: C-D (3, 15) B A A B (4,21) (4,13) (7,21) (4,27) (7,17) (4,21) (2,18) (6, 24) (2,3) (2,16) (6,21) D C (3,15) D C Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

  39. summary • Spanning tree method • Full-mesh topology generation. • Spanning tree construction. • Topology recovery from spanning tree. • Discussion • Perfect encoding vs. upper-bound. • Conservative.

  40. questions

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