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Spanning Tree Method for Link State Aggregation in Large Communication Networks

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

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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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