Jorge Urrutia, IMATE-UNAM E. Chavez, S. Dobrev, E. Kranakis, V. Stacho, J. Opartny, S. Rajsbaum,

Jorge Urrutia, IMATE-UNAM E. Chavez, S. Dobrev, E. Kranakis, V. Stacho, J. Opartny, S. Rajsbaum,

Jorge Urrutia, IMATE-UNAM E. Chavez, S. Dobrev, E. Kranakis, V. Stacho, J. Opartny, S. Rajsbaum,

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Presentation Transcript

1. Local Solutions for Global Problems in Ad-hoc and Wireless Networks Jorge Urrutia, IMATE-UNAM E. Chavez, S. Dobrev, E. Kranakis, V. Stacho, J. Opartny, S. Rajsbaum, G. Salazar, H. Singh, I. Stojmenovic, J. Bose, P. Morin, …

2. Routing in Wireless Networks v u The shortest path problem

3. Routing in Wireless Networks Dijkstra’s algorithm v u The shortest path problem

4. Routing in Wireless Networks Dijkstra’s algorithm v u Optimal solution but … For many current networks is not useful anymore The shortest path problem

5. Routing in Wireless Networks Assumes: a) Stabel network. b) Full knowledge of the network topology Dijkstra’s algorithm v u Optimal solution but … For many current networks is not useful anymore The shortest path problem

6. b Routing tables c d a

7. Other problems to consider: b Routing tables Reliability, maintenance. c g d e f f g b c d e a

8. Other solutions: b a b Message Hi! How are you? -------- -------- -------- -------- Flooding a

9. We would like routing algorithms of the following type:

10. We would like routing algorithms of the following type: a) Local algorithms Take decisions based only on local information stored at the nodes of the network b) No knowledge is assumed on the network other than it is connected

11. We would like routing algorithms of the following type: a) Local algorithms Take decisions based only on local information stored at the nodes of the network b) No knowledge is assumed on the network other than it is connected c) Guarantees delivery of messages

12. We would like routing algorithms of the following type: a) Local algorithms Take decisions based only on local information stored at the nodes of the network b) No knowledge is assumed on the network other than it is connected c) Guarantees delivery of messages d) Messages do not learn much, i.e. they have constant memory.

13. Interval Routing, Santoro and Khatib.

14. Interval Routing, Santoro and Khatib. 8 7 1 9 5 6 [1, 1] 2 [3, 9] 4 3

15. Interval Routing, Santoro and Khatib. [9, 7] 8 8, 8] 7 1 [1, 8] 9 [9, 9] [1, 6] [2, 9] 5 [7, 9] [6,4] 6 [1, 5] [1, 1] 2 [6, 9] [5, 5] [3, 9] [1,2] [5, 3] 4 3 [4, 4]

16. An absent minded, almost memoryless tourist! Shinjuku b a Arrives to Tokio without a map!

17. An absent minded, almost memoryless tourist! Shinjuku b a Arrives to Tokio without a map!

18. An absent minded, almost memoryless tourist! Shinjuku b a Arrives to Tokio without a map!

19. An absent minded, almost memoryless tourist! Shinjuku b a Arrives to Tokio without a map!

20. An absent minded, almost memoryless tourist! Shinjuku b a Arrives to Tokio without a map!

21. Cellular networks   Delaunay triangulation

22. Cellular networks   Delaunay triangulation

23. Cellular networks   Delaunay triangulation

24. Cellular networks   Delaunay triangulation

25. Cellular networks   Delaunay triangulation

26. Cellular networks Reliability   Delaunay triangulation

27. Cellular networks Reliability   Delaunay triangulation

28. Cellular networks Reliability   Delaunay triangulation

29. But most graphs are not Delaunay, trianglations, etc!

30. Face routing  

31. Face routing  

32. Face routing  

33. Face routing  

34. Face routing  

35. Face routing  

36. Face routing  

37. Face routing  

38. Face routing  

39. Face routing  

40. Face routing  

41. Face routing  

42. Face routing  

43. Face routing  

44. Face routing  

45. Face routing  

46. The Model: Unit distance graphs. d=1 Points represent radio stations

47. Unit distance graphs are not planar! The Gabriel subgraph v u Can we planarize them? Using a local algorithm?