1. The Role of Communication Complexity in Distributed Computing Rotem Oshman

2. Background: Distributed Computing

3. Distributed Computing Typical model: – Local computation for free – Charge for “communication”

4. Distributed Lower Bounds

5. Shared Memory Processes communicate by accessing objects in shared memory – Read/write registers – Read-modify-write: CAS, T&S, … Typically asynchronous: – Schedule = sequence of process IDs – Adversarially chosen – Sometimes processes may crash

6. Shared Memory Lower Bounds

7. Message Passing Processes communicate by sending messages – Over some network graph, often complete Fully synchronous, fully asynchronous, or anywhere in between Processes can crash, recover, cheat, lie,… Many successful applications of CC

8. Some differences… Complexity measure Problems Input Distributed Computing Comm. Complexity #rounds (limited bandwidth)total #bits SearchDecision Number-In-HandNumber-on- Forehead (usually)

9. Message-Passing Models MESSAGE-PASSING LOCAL CONGEST SHARED BLACKBOARD #rounds total CC

10. Talk Overview I.Lower bound techniques a.CONGEST (#rounds): reductions from 2-party communication complexity b.Total CC with private channels II.Shared blackboard a.Number-in-hand b.“Not-quite-number-in-hand”

11. The CONGEST Model

14. CONGEST Lower Bounds for Arbitrary Graphs … by reduction from 2-party disjointness

15. 2-Party Reductions

17. Example: Approximate Diameter

18. Lower Bound

19. 1 2 …

20. 1 2 …

21. Approximate Diameter

22. Multi-Player NIH Communication with Private Channels

23. The Message-Passing Model

24. The Coordinator Model

25. Message-Passing vs. Coordinator Secure multi-party computation!

26. Message-Passing Lower Bounds

27. Symmetrization [Phillips, Verbin, Zhang ’12]

29. Symmetrization Example: Bitwise-XOR

30. Set Disjointness ?

31. Symmetrization vs. Disjointness

32. [BEOPV’13] Lower Bound Outline

33. Info Cost for Multi-Player

34. Reduction from D ISJ to graph connectivity [Based on WZ’13] (Players)(Elements)

35. Number-In-Hand Shared Blackboard

36. Why Should We Care? Some fundamental question still open Natural model for distributed computing – Single-hop wireless network – More generally, abstracts away network topology – Related to MapReduce, etc. [Hegeman and Pemmaraju’14]

37. Example: NIH Multi-Party Disjointness

38. “Not-Quite Number in Hand”

40. 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

41. 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

42. 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

43. Simulating the Algorithm

44. More complicated….

45. Upper Bound on Subgraph Detection

46. Detecting Triangles

47. Triangles to 3-Party NOF Disjointness

50. 3-Party NOF Disjointness

51. Conclusion MESSAGE-PASSING LOCAL CONGEST SHARED BLACKBOARD #rounds total CC

52. Directions for Future Research Exploiting asynchrony and faults to get stronger communication lower bounds

53. Example 1: Dynamic Networks

55. Example 2: Byzantine Consensus