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

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Presentation on theme: "Spanning Tree Method for Link State Aggregation in Large Communication Networks Whay Choiu Lee."— Presentation transcript:

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(n 2 ) ). 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 A B C D (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

6 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 C D (7,10) (4,8) (7,7) (5,5) (9,8) (3,4) (4,7) (6,6) (2,3) (10,5)

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

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

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. Maximum weight spanning tree: d <= min(a,b,c) Minimum weight spanning tree: d >= max(a,b,c) A B C D b a 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 Representation shortest-widest routing algorithm A B C D (7,10) (4,8) (7,7) (5,5) (9,8) (3,4) (4,7) (6,6) (2,3) (10,5)

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

14 Constructing Maximum-Bandwidth Full-Mesh Representation shortest-widest routing algorithm A B C D (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)

15 Constructing Maximum-Bandwidth Full-Mesh Representation shortest-widest routing algorithm A B C D (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)

16 Constructing Maximum-Bandwidth Full-Mesh Representation shortest-widest routing algorithm A B C D (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)

17 Constructing Maximum-Bandwidth Full-Mesh Representation shortest-widest routing algorithm A B C D (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)

18 Constructing Maximum-Bandwidth Full-Mesh Representation shortest-widest routing algorithm A B C D (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)

19 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 C D (6,24) (7,17) (6,21) (4,27) (4,18) (4,13)

20 Deriving Maximum-Weight Spanning Tree for Bandwidth greedy 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 Deriving Maximum-Weight Spanning Tree for Bandwidth greedy algorithm 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 C D (6,24) (7,17) (6,21) (4,27) (4,18) (4,13)

22 Deriving Maximum-Weight Spanning Tree for Bandwidth greedy algorithm A B C D (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)

23 Deriving Maximum-Weight Spanning Tree for Bandwidth greedy algorithm A B C D (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)

24 Deriving Maximum-Weight Spanning Tree for Bandwidth greedy algorithm A B C D (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)

25 Maximum-Weight Spanning Tree for Bandwidth A B C D 6 7 6 44 4

26 Maximum-Weight Spanning Tree for Delay A B C D 24 17 21 2718 13

27 Decoding Maximum-Weight Spanning Tree for Bandwidth depth-first-search A B C D 6 7 6 44 4 Root A

28 Decoding Maximum-Weight Spanning Tree for Bandwidth depth-first-search A B C D 6 7 6 44 4 Root A: E(AD)

29 Decoding Maximum-Weight Spanning Tree for Bandwidth depth-first-search A B C D 6 7 6 44 4 Root A: E(AD), E(AC)

30 Decoding Maximum-Weight Spanning Tree for Bandwidth depth-first-search A B C D 6 7 6 44 4 = min(6,4) Root A: E(AD), E(AC), E(CB)

31 Decoded Full-Mesh for Bandwidth A B C D 6 7 6 44 4

32 Decoded Full-Mesh for Delay A B C D 24 21 2721

33 Discussion: Full-Mesh Topology Comparison A B C D (6, 24) (7,21) (6,21) (4,27) (4,21 ) (4,18) c A B C D (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)

34 Full-Mesh Topology Comparison A B C D (6, 24) (7,21) (6,21) (4,27) (4,21 ) (4,18) c A B C D (6,24) b (7,17) a (6,21) ( 4,27 ) d (4,13) 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 A B C D (6, 24) (7,21) (6,21) (4,27) (4,21 ) A B C D (2,16) (7,17) (3,15) ( 2,18 ) (2,3) (4,13) Minimum-Delay Full-Mesh Decoded Maximum-Bandwidth Full-Mesh

36 Discussion: Full-Mesh Topology Problem A B C D (6, 24) (7,21) (6,21) (4,27) (4,21 ) A B C D (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)

37 Discussion: Full-Mesh Topology Problem A B C D (6, 24) (7,21) (6,21) (4,27) (4,21 ) A B C D (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)

38 Discussion: Full-Mesh Topology Problem A B C D (6, 24) (7,21) (6,21) (4,27) (4,21 ) A B C D (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)

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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