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CS710

CS710. INFOCOM 2007 Disjoint Multipath Routing to Two Distinct Drains in a Multi-Drain Sensor Network Preetha Thulasiraman, Srinivasan Ramasubramanian and Marwan Krunz University of Arizona. September 16, 2008. Shinae Woo. Multipath routing for WSN. Disjoint multipath routing!.

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CS710

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  1. CS710 INFOCOM 2007 Disjoint Multipath Routing to Two Distinct Drains in a Multi-Drain Sensor Network Preetha Thulasiraman, Srinivasan Ramasubramanian and Marwan Krunz University of Arizona September 16, 2008 Shinae Woo

  2. Multipath routing for WSN Disjoint multipath routing! Sensor node Drain

  3. Problem definition • DRMD-2 problem • Disjoint Routing in a Multi-Drain network • |D| trees, each rooted at a distinct drain • Every node has two node-disjoint path to two distinct drain 2 2 2 2 6 5 6 5 6 6 5 5 c 7 4 c 7 4 c c 7 7 4 4 3 3 3 3 b 8 b 8 b b 8 8 1 1 1 1 9 a 9 a 9 9 a a

  4. Colored tree • Two trees rooted at a drain • Every node has a two disjoint path to the drain a b c a b c 7 8 9 7 8 9 4 5 6 4 5 6 1 1 2 3 2 3 Red tree Blue tree

  5. Construction of colored tree 1 7 2 9 3 6 4 5 8 Theorem Graph G is 2-node connected -> G has a solution of colored tree

  6. Removing backtracking 1 1 2 (1,3) • generalized low-point • Lowest DFS-index traversing a sequence of nodes increasing DFS-index with the exception of last hop • Value (GLPV), path , neighbor (GLPN) • Provide shorter path than low-point 7 (1,4) 3 2 (1,5) 4 9 3 6 Back edge 5 (1,6) 4 (1,7) (6,9) 6 8 5 8 (1,1) 7 9 (6,6)

  7. Colored tree for two drains • Every node has a path to the two drains that are node-disjoint 2 2 7 8 7 8 3 6 9 3 6 9 4 5 a 4 5 a 1 1 c b c b

  8. Solution for colored tree to two drains • Make a virtual drain d • Make a colored tree • One tree is rooted at drain 1, the other tree is rooted at drain 2 • Remove virtual drain 2 2 2 2 7 7 8 8 7 7 8 8 2 3 3 6 6 9 9 7 3 3 8 6 6 9 9 4 4 5 5 a a 3 6 4 4 9 5 5 a a d d d 1 1 1 1 c c b b 4 5 a c c b b 1 c b

  9. Problem definition review • DRMD-2 problem • Pairs of two distinct drains |D|C2  O(|D|^2) 2 2 2 6 5 6 5 6 5 c 7 4 c 7 4 c 7 4 3 3 3 b 8 b 8 b 8 1 1 1 9 a 9 a 9 a

  10. CTMP problem • |D| tree pairs • ( a primary drain, the other secondary drains) • (d1, {d2, d3}) , (d2, {d1, d3}) , (d3, {d1, d2}) • Every node has a tree pair • Two paths to a primary drain and one of the secondary drain are node-disjoint 2 2 2 6 5 6 6 5 5 c 7 4 c c 7 7 4 4 S S S 3 3 3 b 8 b b 8 8 1 1 1 9 a 9 9 a a

  11. Integer programming V P S P S P S 2 2 2 6 5 6 5 6 5 c 7 4 c 7 4 c 7 4 3 3 3 b 8 b 8 b 8 1 1 1 9 a 9 a 9 a 6 5 c 7 4 b 8 9 a

  12. Distributed Algorithm • Distributed DFS numbering • Distributed path augmentation • Node which has TOKEN initiate path search • Each node forwarding SEARCH message • To find a new path • If there are no neighbor to initiate path search, passing TOKEN to another node • If there are no more node to passing TOKEN, it complete. • Graph Selection • Choose a tree pair among |D| tree pairs

  13. Distributed DFS numbering 3 Low-point table (to each drain) Example of node 4 4 – 7 – 8 – 9 – d1 4 – 7 – b – d2 4 – 7 – 8 – d3 4 5 2 2 6 5 6 1 c 7 4 7 3 b 8 8 1 9 a (1,7) 9 b (1,1) a c Back edge Forwarding edge

  14. Distributed path augmentation • (d3, {d1, d2}) 2 2 2 6 5 6 5 6 5 c 7 4 c 7 4 c 7 4 token 3 3 3 b 8 b 8 b 8 1 1 1 9 a 9 a 9 a

  15. Graph Selection • |D| tree pairs • Each has two tree • One is rooted at primary drain (red tree) • The other is rooted at one of secondary drains (blue tree) • Calculate the path length to each tree • Each node choose the tree pair which has the smallest average path length (of red tree and blue tree) • ⌈ log|D| ⌉ bits for choosing tree pairs • 1 bits for choosing red or blue tree

  16. Comparing with optimal solution Average path lengths # of nodes

  17. Distinct drains vs. Same drain Average path lengths # of nodes 50 100 300 1 out of n 2 out of n

  18. Conclusion • Objective • Constructing multiple trees rooted at distinct drains • Every node has a path to two drains which are node-disjoint • Contributions • Solve CTMP problem • O(|L|) time complexity • O(|D||L|) message complexity • Significant path length reduction • Compared with sending to one out of multiple drain

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