Network-Aware Distributed Algorithms for Wireless Networks

1. Network-Aware Distributed Algorithmsfor Wireless NetworksNitin VaidyaElectrical and Computer EngineeringUniversity of Illinois at Urbana-Champaign

3. Multi-Channel Wireless Networks:Theory to Practice Nitin Vaidya Electrical and Computer Engineering University of Illinois at Urbana-Champaign

4. Wireless Networks • Infrastructure-Based Networks • Infrastructure-Less (and Hybrid) Networks: • Mesh networks, ad hoc networks, sensor networks

5. What Makes Wireless Networks Interesting? Broadcast channel Interference management non-trivial Signal-interference are relative notions power D B C A Interference Signal

6. What Makes Wireless Networks Interesting? Many forms of diversity Time Route Antenna Path Channel

7. What Makes Wireless Networks Interesting? Antenna diversity D C A B Sidelobes not shown

8. What Makes Wireless Networks Interesting? Path diversity x1 x2 y1 y2

9. High interference D B C A D B C A Low interference What Makes Wireless Networks Interesting? Channel diversity Low gain B A B A High gain

10. Research Challenge Dynamic adaptation to exploit available diversity

11. capacity User Applications Multi-channel protocol channels Capacity & Scheduling Insights on protocol design Fixed D IP Stack OS improvements Software architecture Net-X testbed F B ARP E Switchable A Channel Abstraction Module C Interface Device Driver Interface Device Driver Net-XMulti-Channel Wireless MeshTheory to Practice

13. Secret to happiness is to lower your expectations to the point where they're already met with apologies to Bill Watterson (Calvin & Hobbes)

14. Network-Aware Distributed Algorithmsfor Wireless NetworksNitin VaidyaElectrical and Computer EngineeringUniversity of Illinois at Urbana-Champaign

15. Distributed Algorithms & Communications Communications / Networking Distributed Algorithms

16. Distributed Algorithms & Communications • Problems with overlapping scope • But cultures differ Communications / Networking Distributed Algorithms

17. Communications / Networking Distributed Algorithms Emphasis on “exact”performance metrics Constants matter Black box networks Emphasis onorder complexity

18. Communications / Networking Distributed Algorithms Emphasis on “exact”performance metrics Constants matter Information transfer(typically “raw” info) Black box networks Emphasis onorder complexity

19. Communications / Networking Distributed Algorithms Black box networks Emphasis onorder complexity Emphasis on “exact”performance metrics Constants matter Information transfer(typically “raw” info) Computationaffects communication

20. Distributed Algorithms & Communications Communications / Networking Distributed Algorithms

21. Outline Two distributed algorithms • Byzantine agreement • Scheduling (CSMA) Rate Region Communications / Networking Distributed Algorithms

22. Rate Region • Defines the way links may share channel • Interference posed to each otherdetermines whether a set of linksshould be active together

23. “Ethernet” Rate Region sum-rateconstraint S Rate S2 1 2 Rate S1 Private channelsS1 and S2 Rate S1 + Rate S2 ≤ C R1 +R2 ≤C

24. Point-to-Point NetworkRate Region Rij≤ Capacity ij S Each directed linkindependent of other links 1 2

25. Wireless Network: Rate Region • Some links share channel with each otherwhile others don’t R2 R1 R3 3 4 1 2 max(R1/C1 , R3/C3) + (R2/C2) ≤1

26. Broadcast Channel:Rate Region 1 R ≤ C1 2 S 3

27. Broadcast Channel:Rate Region 1 R ≤ C2 > C1 2 S “Range” varies inverselywith rate 3

28. Broadcast Channel 1 1 R12 2 2 S S R1 R2 3 3 R1/C1 + R2/C2 + R12/C12 ≤1

29. Outline Two distributed algorithms • Byzantine agreement • Scheduling (CSMA)

30. Impact of Rate Region • Network rate region affectsability to performmulti-party computation • Example: Byzantine agreement (broadcast)

31. Byzantine Agreement: Broadcast Source S wants to send message to n-1 receivers • Fault-free receivers agree • S fault-free agree on its message • Up to f failures

32. Impact of Rate Region • How does rate region affectbroadcast performance ? • How to quantify the impact ?

33. Throughput of Agreement • Borrow notion of throughputfrom communications literature • b(t) = number of bits agreed upon in [0,t] Long timescale measure

34. Capacity of Agreement • Supremum of achievable throughputsfor a given rate region

35. Broadcast Channel Rate region R ≤ C 1 2 S Agreement capacity = C R 3

36. “Ethernet” Rate Region • Sum ofprivate link capacities ≤ C S 1 3 C 2 Agreement capacity = Communication complexityper agreed bit

37. “Ethernet” Rate Region Communication complexity per-agreed bit number of bits required to agree on L bits = L

38. “Ethernet” Rate Region Communication complexity per-agreed bit number of bits required to agree on L bits = L

39. “Ethernet” Rate Region Communication complexity per-agreed bit • L = 1 : Ω(n2) for n node [Dolev-Reischuk] (deterministic algorithms) number of bits required to agree on L bits = L

40. “Ethernet” Rate Region Communication complexity per-agreed bit • L = 1 : Ω(n2) for n nodes • L  ∞ : can be shown O(n) (multi-value agreement) number of bits required to agree on L bits = L

41. “Ethernet” Rate Region Communication complexity per-agreed bit • L = 1 : Ω(n2) for n nodes • L  ∞ : can be shown O(n) (multi-value agreement) number of bits required to agree on L bits = L bits per agreed-bit n(n-1) 41 (n-f)

42. “Ethernet” Rate Region • Sum ofprivate link capacities ≤ C S 1 3 (n-f) C Agreement capacity ≥ 2 n(n-1) Conjecture: tight bound

43. Point-to-Point Network Each link has its own capacity Load ij ≤ Cij S A C B

44. Point-to-Point Network Each link has its own capacity Cij as shown Agreement Capacity ? S 4 4 2 A C 3 3 4 4 B 3 3

45. Point-to-Point Network Cij as shown Agreement Capacity = 2 S 4 4 2 A C 3 3 4 4 B 3 3

46. Point-to-Point Network Cij as shown Agreement Capacity = 6 є S 4 4 2 A C 3 3 4 4 B 3 3

47. Point-to-Point Network Capacity-achieving scheme for Arbitrary 4 nodenetworks S A C Approach: • Upper boundbasedon min-cuts • Lower bound usingcoding B

48. Point-to-Point Network Capacity-achieving scheme for Arbitrary 4 nodenetworks S A C Minimum numberof rounds requireddepends on linkcapacities B

49. Point-to-Point Network Capacity-achieving scheme for Arbitrary 4 nodenetworks S A C B Open problem:Everything else

50. Open Problems • Capacity-achieving agreement withgeneral rate regions • Subset of nodes as “receivers”