Routing Algorithms using Random Walks with Tabu Lists

1. Routing Algorithms using Random Walks with Tabu Lists KarineAltisen & Stéphane Devismes Joint work with Antoine Gerbaud, Pascal Lafourcade, and ClémentPonsonnet ARESA 2

2. Disclaimer • Today, we will speak about probabilities • But, we are not specialists … Meeting Synchrone

3. Wireless Sensor Network (WSN) Sensor(s) Processor Radio Battery Meeting Synchrone

4. Routing Meeting Synchrone

5. Application Meeting Synchrone

6. Setting • One sink/Multi source • Connected • Identified • Reliable • Asynchronous • Spontaneous requests 8 4 7 3 5 9 1 6 2 Meeting Synchrone

7. Random Walk 8 4 7 3 5 9 1 Rand(9,8,6,4,3) Rand(1,7,5,6,2) 6 Rand(7,9,2) 2 Rand(1,9,6) Meeting Synchrone

8. Probability Laws • Uniform (RW) • Let v,u two neighbors, vu • Problem: hitting time = O(N3) Meeting Synchrone

9. Probability Laws • Biased (Yamashita et al) (RWLD) • Let v,u two neighbors, vu • standardize frequencies of visits, for all nodes • hitting time = O(N2) Meeting Synchrone

10. RW vs. RWLD Meeting Synchrone

11. Routing by Random Walk • Pros • Message length • Tight local computation and memory • No need of overlay • Load of the network • … • Cons • Hitting time • (average number of hops to reach the sink) • O(N3) (RW) and O(N2) (RWLD) Meeting Synchrone

12. Random Walk with Tabu Lists • Add memory to help random walks • Avoid cycles • Store hints about previous choices • ≤k where k is small • Good trade-off ? Meeting Synchrone

13. Where ? • Messages • Store IDs of visited nodes • Visit new nodes first • Nodes • One list per destination • Store message ID • Detect cycles •  cycle detections: visits  Meeting Synchrone

14. Full ? (Update policy) • FIFO policy • Rand policy Meeting Synchrone

15. FIFO Policy • Update(e,L) e Meeting Synchrone

16. Rand Policy • Update(e,L) Rand Meeting Synchrone

17. Sum up • Probability law: RW / RWLD • Tabu Lists Location: node / message • Tabu List size • Update policies: FIFO / Rand Meeting Synchrone

18. Tabu List in Messages (TLM) 8 4 7 3 5 9 [9,5] [2,9] 1 Rand(8,6,4,3) = 3 [1,2] [2,9] Rand(7,5,6)=5 6 Rand(7,9,2)=2 2 [1] [1] [1,2] Rand(9,6) = 9 Meeting Synchrone

19. Tabu List & Counters in Nodes (TLCN)(1/2) 1 (12,1) (12,1) (23,8) (23,8) 12 1 (23,8) 1 2 (12,1) (23,8) Meeting Synchrone 2 1 1

20. Tabu List & Counters in Nodes (TLCN)(2/2) • Next destination ? Meeting Synchrone

21. Experimentations (settings) • Sinalgo (JAVA) • Graphs: UDG, connected, one sink/multi-source, uniform distribution • 100 messages per sources • Data generation: [400..600] • Transmission time: [40..50] • List sizes: • TLM: 1 & 15 • TLCN: 15 • Random Walk: RWLD • Update: FIFO & Rand Meeting Synchrone

22. Hitting time (1/2) Meeting Synchrone

23. Hitting time (2/2) Meeting Synchrone

24. Volume, e.g., sum |messages| Meeting Synchrone

25. Convergence of TLCN Meeting Synchrone

26. Sum up Meeting Synchrone

27. Analysis Meeting Synchrone

28. NSC for TLM • NSC: update rule  finite average hitting time “If the list is full and the current node is not in the list, then the probability of removing the oldest element is positive” FIFO and Rand match the NSC Meeting Synchrone

29. RW+TLM vs. RW (1/2) • |List| ≥ 3, there exist graphs where RW is better than RW+TLM • Ex. for 4 … Meeting Synchrone

30. RW+TLM vs. RW (2/2) • |List| = 1,2, RW+TLM is always better than RW 2 3 9 7 4 1 RW+TLM RW Meeting Synchrone

31. RWLD+TLM vs. RWLD (1/2) • For all size, there exist graphs where RWLD is better than RWLD+TLM • |List| ≥ 3, as previously • 2, to be done ! • 1: Meeting Synchrone

32. RWLD+TLM vs. RWLD (2/2) • Conjecture: In random graphs, RWLD+TLM is always better than RWLD Meeting Synchrone

33. RW+TLM 1,2 vs. RWLD (2/2) • There exist graphs where RWLD is better than RW+TLM Meeting Synchrone

34. TLCN • Is the hitting time finite ? In case ∞+asynchronous, no Sink 1 ∞ Source Meeting Synchrone

35. Thank you Meeting Synchrone