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The Role of Communication Complexity in Distributed Computing Rotem Oshman.

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Presentation on theme: "The Role of Communication Complexity in Distributed Computing Rotem Oshman."— Presentation transcript:

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

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

15 2-Party Reductions

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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]

28

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”

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43 Simulating the Algorithm

44 More complicated….

45 Upper Bound on Subgraph Detection

46 Detecting Triangles

47 Triangles to 3-Party NOF Disjointness

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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

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55 Example 2: Byzantine Consensus

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