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Consensus and Collision Detectors in Wireless Ad Hoc Networks
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  1. Consensus and Collision Detectorsin Wireless Ad Hoc Networks

  2. Consensus and Collision Detectorsin Wireless Ad Hoc Networks

  3. Consensusand Collision Detectorsin Wireless Ad Hoc Networks

  4. Wireless Ad Hoc Networks

  5. Wireless Ad Hoc Networks • Challenges: • Unknown number • No unique ids • Fault-prone • Collision-prone communication

  6. Wireless Ad Hoc Networks • Challenges: • Unknown number • No unique ids • Fault-prone • Collision-prone communication

  7. How to solve problems • in wireless ad hoc networks with • unreliable communication?

  8. How to solve consensus • in wireless ad hoc networks with • unreliable communication? • Consensus: • Fundamental agreement problem • in fault-tolerant computation

  9. Outline • Introduction • Collision-prone Networks • Collision Detectors • Algorithms and Lower Bounds • Conclusions

  10. Single-hop network • Synchronous rounds • Unknown number of nodes • No unique identifiers

  11. Single Broadcast

  12. Single Broadcast

  13. “Ethernet” Collisions

  14. “Ethernet” Collisions ? ? ? ? ? ? ? ? ? ?

  15. More Realistic Collisions

  16. More Realistic Collisions ? ?

  17. Unfortunately… • Consensus is impossible with • non-uniform collisions.

  18. Collision Detection

  19. Collision Detection ! ! ! ! !

  20. Collision Detection ! ! ! ! ! • Receiver-centric • How many messages lost? • Who sent lost message?

  21. Collision Detector Classes If ½ messages are lost, then report collision. If all messages are lost, then report a collision. Consensus is impossible with C

  22. Consensus with CD V is the value domain

  23. Consensus with CD (Always) Accurate V is the value domain

  24. Consensus with CD Eventually Accurate V is the value domain

  25. Eventual Collision Freedom • Eventually, if only 1 node broadcasts…

  26. Eventual Collision Freedom • Eventually, if only 1 node broadcasts, then no collision occurs. • Use a contention manager. • Outputs “active/passive” at each node. • Implementation: randomized backoff, e.g.

  27. Eventual Collision Freedom • Eventually, if only 1 node broadcasts*, then no collision occurs. • Use a contention manager. • Outputs “active/passive” at each node. • Implementation: exponential backoff, e.g. • If ≤ b nodes broadcast, then no collisions. • b is an unknown MAC layer constant • b could be as low as 1

  28. Consensus with CD V is the value domain

  29. Consensus with CD V is the value domain

  30. Consensus with CD V is the value domain

  31. Consensus with AC • Algorithm executes in super-rounds: • Round 1: • Active nodes vote on a value. • Round 2: • Veto round. • Anybody can veto.

  32. Consensus with AC v2 v1 v2 Round 1

  33. Consensus with AC v2 v1 v2 Round 1

  34. Consensus with AC v2 {v1} v1 v2 Round 1

  35. Consensus with AC v1 v1 v2 Round 1

  36. Consensus with AC v1 v1 {v2} v2 Round 1

  37. Consensus with AC v1 v1 v2 Round 1

  38. Consensus with AC v1 v1 v2 {v2, } Round 1

  39. Consensus with AC v1 v1 v1 v1 v2 v2 Round 1 Round 2

  40. Consensus with AC v1 v1 veto v1 v1 veto v2 v2 • Continue… Round 1 Round 2

  41. Consensus with AC v1 v1 v2 Round 1

  42. Consensus with AC v1 v1 v2 Round 1

  43. Consensus with AC v1 v1 {v1} v2 Round 1

  44. Consensus with AC v1 v1 v2 Round 1

  45. Consensus with AC v1 v1 v2 {v1} Round 1

  46. Consensus with AC v1 v1 v1 Round 1

  47. Consensus with AC v1 v1 v1 v1 v1 v1 Round 1 Round 2

  48. Consensus with AC v1 v1 Decides at most 3 rounds after stabilization* *Stabilization: accuracy and collision-freedom v1 v1 v1 v1 Decide v1 Round 1 Round 2