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TexPoint fonts used in EMF.

Deterministic Multi-Channel Information Exchange. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box .: A A A A A A A A A A. n:= # nodes. Problem :. n:= # nodes k:= # information. Problem :. Have information. ?. Disseminate to all!.

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TexPoint fonts used in EMF.

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  1. Deterministic Multi-Channel Information Exchange TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAA

  2. n:= # nodes Problem:

  3. n:= # nodes k:= # information Problem: Have information ? Disseminate to all!

  4. Problem: ? Disseminate to all!

  5. Problem: ? Disseminate to all!

  6. n:= # nodes Problem: 1 5 2 3 Unique IDs 1…n 4 n

  7. Problem: ? Disseminate to all! Easy: O(n) Faster?

  8. I can: send / receive reacheachnode

  9. I can: ? send / receive reacheachnode

  10. I can: send / receive reacheachnode nocollisiondetection

  11. I can: send / receive reacheachnode nocollisiondetection 101 Mhz 117 Mhz 132 Mhz … switchchannels synchronus

  12. I can: complexity computation: free radio: time 1 send / receive reacheachnode nocollisiondetection switchchannels synchronus

  13. n:= # nodes k:= # information k

  14. n:= # nodes k:= # information k k

  15. n:= # nodes k:= # information k k Optimal

  16. n:= # nodes k:= # information k k Optimal ????

  17. n:= # nodes k:= # information [HPSW11] - Channels needed for time O(k):

  18. n:= # nodes k:= # information [HPSW11] - Channels needed for time O(k): This paper:

  19. n:= # nodes k:= # information randomized [HPSW11] - Channels needed for time O(k): This paper:

  20. n:= # nodes k:= # information randomized [HPSW11] - Channels needed for time O(k): deterministic This paper:

  21. n:= # nodes k:= # information randomized [HPSW11] - Channels needed for time O(k): deterministic This paper: Optimal? Optimal? Optimal? Optimal?

  22. n:= # nodes k:= # information randomized [HPSW11] - Channels needed for time O(k): deterministic This paper: k

  23. Main ingredient: Specially taylored graphs.

  24. Main ingredient: Specially taylored graphs. (Inspired by use of lossless expanders in [CK08])

  25. Main ingredient: Specially taylored graphs. (Inspired by use of lossless expanders in [CK08]) Topology: Still single hop. Graphs used to select channel.

  26. Bipartite : node IDs new names 1 5 2 6 3 7 4

  27. Bipartite : node IDs new names 1 5 2 6 3 7 4

  28. Matching Graphs: • Nodes in V have degee

  29. Matching Graphs: • Nodes in V have degee • Fixed order of edges

  30. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor.

  31. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 5 2 6 i 3 have unique i-neighbor 7 i 4

  32. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 5 2 6 i 3 have unique i-neighbor 7 i 4

  33. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 1 2 5 2 2 1 6 2 3 1 7 2 4 1

  34. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 1 2 5 2 2 1 6 2 3 1 X 7 2 4 1

  35. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 1 5 2 1 6 3 1 X 7 4 1

  36. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 1 5 2 1 6 3 1 X 7 4 BAD 1

  37. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 1 2 5 2 2 1 6 2 3 1 X 7 2 4 1

  38. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 2 5 2 2 6 2 3 X 7 2 4

  39. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 2 5 2 2 6 2 3 X 7 2 GOOD 4

  40. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 1 X 5 2 1 6 3 1 7 4 1

  41. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most k there is at least nodes in X have a unique i-neighbor. 1 1 X 5 2 1 6 3 1 7 4 1

  42. Matching Graphs: • Nodes in V have degee • Fixed order of edges • For any of size at most K there is at least nodes in X have a unique i-neighbor. 1 1 2 5 2 2 1 exist if 6 2 3 1 7 2 4 1

  43. What are these graphs good for?

  44. What are these graphs good for? Renaming

  45. What are these graphs good for? Renaming 1 1 2 5 2 2 1 6 2 3 1 7 2 4 1

  46. What are these graphs good for? Renaming • To each of the k «reporters» we can assing a new unique name in |W| in time O( using |W| channels. 1 1 2 5 2 2 1 6 2 3 1 7 2 4 1

  47. What is renaming good for?

  48. What is renaming good for? Assignment of reporters to channels!

  49. What is renaming good for? Assignment of reporters to channels! Example: k < log n

  50. What is renaming good for? Assignment of reporters to channels! Example: k < log n Original names n

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