1. Fault tolerance and related issues in distributed computing Shmuel Zaks zaks@cs.technion.ac.il GSSI - Feb 20161

2. 2 Haifa

3. GSSI - Feb 20163 CS, Technion

4. Part 0: Part 0: Distributed computing – an overview: basic notions; seminar focus: from lower bounds, via impossibility, to fault tolerance and self-stabilization. Part 1: Part 1: Lower bounds Part 2: Part 2: Computing in spite of faults - impossibility of consensus Part 3: Part 3: Detecting faults - the snapshot algorithm Part 4: Self-stabilization - Self recovery from faults GSSI - Feb 20164

5. Part 0: Part 0: An overview Part 1: Part 1: Lower bounds Part 2: Part 2: Computing in spite of faults Part 3: Part 3: Detecting faults Part 4: Part 4: Self-stabilization GSSI - Feb 20165

6. processors communication problem Communication network GSSI - Feb 20166 A. The model

7. Anonymous GSSI - Feb 20167

8. 12 a e 6 c Unique identities GSSI - Feb 20168

9. d a e b c message passing communication lines, channels topology communication GSSI - Feb 20169

10. ab c d e directed, undirected (message passing) GSSI - Feb 201610

11.  message delivery mechanism  fifo  reliable, no faults  finite, arbitrary delay  queues of messages (message passing) GSSI - Feb 201611

12. Distributed algorithm, protocol  Send a message  receive a message  do local computation GSSI - Feb 201612 (message passing) Execution

13. R4R4 GSSI - Feb 201613 R1R1 R2R2 R3R3 R5R5 e a b d c shared memory

14. 7 2 31 25 9 88 40 9 A B read/write (shared memory) GSSI - Feb 201614

15. synchronization Synchronous, Asynchronous d a e b c GSSI - Feb 201615

16. Asynchronous Model GSSI - Feb 201616 ij time t+???time t Clock Network (synchronization)

17. Synchronous Model GSSI - Feb 201617 ij time t+dtime t Clock Network (synchronization)

18. Asynchronous Model - many executions GSSI - Feb 201618 Synchronous Model - unique execution rounds (synchronization)

19. Asynchronou s GSSI - Feb 201619 Synchronous Shared memory Message passing (synchronization)

20. GSSI - Feb 201620 Asynchronous model: for correctness, for upper bound analysis Synchronous model: for lower bound analysis

21. Topology GSSI - Feb 201621 Ring d a e b c

22. Clique d a e b c (Topology) GSSI - Feb 201622

23. 7 2 31 25 9 88 40 12 4 General (Topology) GSSI - Feb 201623

24. Why simple networks? They enable the understanding of many design issues In existing general networks – assume a virtual simple network implemented (e.g. a ring) (Topology) GSSI - Feb 201624

25. Complexity measures GSSI - Feb 201625  Synchronous system  time  Asynchronous system  communication  communication (messages, bits)  time (synchronous time, longest chain, bounded delay)

26. Parallel vs. Distributed computing Parallel computing – given a problem … (ex: sorting) Distributed computing – Given a network … (ex: broadcast) GSSI - Feb 201626

27. (Parallel vs. Distributed computing( Parallel computing : time vs. number of processors Distributed computing: number of messages Complexity goals: Parallel computing: efficiency Distributed computing: correctness GSSI - Feb 201627

28. problem, task P1P1 P2P2 P3P3 input output 3 7 5 Leader election yes no consensus 1 0 0 1 1 1 GSSI - Feb 201628 b. Problems

29. issues GSSI - Feb 201629  design and analysis of algorithms  impossibility, lower bounds  fault tolerance

30. problems GSSI - Feb 201630  broadcast  snapshot  consensus  shortest path, maximal flow  leader election, breaking symmetry, maximum finding, spanning tree, center  termination  deadlock

31. Example: broadcast GSSI - Feb 201631 d a e b c f

32. Broadcast: bfs (breadth-first-search) GSSI - Feb 201632 d a e b c f

33. Broadcast: dfs (depth-first-search) GSSI - Feb 201633 d a e b c f

34. message complexity  each edge carries exactly one message at each direction  message complexity is 2|E| GSSI - Feb 201634

35. time complexity GSSI - Feb 201635 synchronous time 2|E| longest chain 2|E| bounded delay 2|E|

36. pi (propogation of information), shout-echo GSSI - Feb 201636 d a e b c f

37. Algorithm pi ( p ropogation of i nformation) send m to each neighbour stop GSSI - Feb 201637 if receive m along edge e: send m on all edges except e stop

38. pi Theorem: The following holds for every execution of the pi algorithm: A processor receives the message m at most once. The execution terminates. each processor receives the message m. The edges on which processors receive m form a spanning tree. The message complexity is 2|E|-|V|+1. The time complexity … GSSI - Feb 201638

39. pif (propogation of information with feedback) shout-echo GSSI - Feb 201639 d a e b c f

40. Distributed algorithms “Positive” results: design, analysis, upper bounds “Negative” results: lower bounds, impossibility GSSI - Feb 201640 c. In this seminar

41. P1P1 P2P2 P3P3 input output 3 7 5 Leader election yes no GSSI - Feb 201641 Part 1: Part 1: Lower bounds

42. GSSI - Feb 201642 message passing asynchronous 9 4 5 8 6 ? x x x x Leader election

43. 9 4 5 8 6 GSSI - Feb 201643 We’ll see: a lower bound of Ω (n log n) messages

44. GSSI - Feb 201644 d a e b c f Lower bound and fault tolerance Usually all processors need to compute some function Lower bound of Ω(|E|) g

45. problem, task P1P1 P2P2 P3P3 input output consensus 1 0 0 1 1 1 GSSI - Feb 201645 Part 2: Part 2: Computing in spite of faults

46. message passing asynchronous 0 1 1 0 1 Consensus GSSI - Feb 201646 We’ll see: impossibility to reach consensus.

47. GSSI - Feb 201647 Snapshot Part 3: Part 3: Detecting faults

48. GSSI - Feb 201648 We’ll see: snapshot algorithm.

49. GSSI - Feb 201649 Example: clock synchronization 66 6 6 6 7 7 7 7 7 Part 4: Self-stabilization

50. GSSI - Feb 201650 67 6 4 6

51. 4 Let’s try … 6 6 6 7 GSSI - Feb 201651

52. 4 But … 6 6 6 7 GSSI - Feb 201652

53. GSSI - Feb 201653 67 6 4 6 We’ll see: self stabilizing algorithms, proofs and performance analysis.