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Teacher: Chun-Yuan Lin

Introduction to Distributed Algorithm Part Two: Fundamental Algorithm Chapter 6- Wave and Traversal Algorithms. Teacher: Chun-Yuan Lin. Wave and Traversal Algorithms (1).

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Teacher: Chun-Yuan Lin

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  1. Introduction to Distributed AlgorithmPart Two: Fundamental AlgorithmChapter 6- Wave and Traversal Algorithms Teacher: Chun-Yuan Lin Wave and Traversal Algorithms

  2. Wave and Traversal Algorithms (1) • In the design of distributed algorithms for various applications several very general problems for process networks appear frequently as subtasks. • broadcasting of information • achieving a global synchronization between processes • triggering the execution of some event in each process • computing a function of which each process holds part of the input • These tasks are so fundamental that solutions to more complicated problems • election (Chapter 7) • termination detection (Chapter 8) Wave and Traversal Algorithms

  3. Wave and Traversal Algorithms (2) • The importance of message-passing schemes, called wave algorithms • This chapter formally defines wave algorithms (Subsection 6.1.1) • proves some general results about them (Subsection 6.1.2) • The observation that the same algorithms can be used for all of the fundamental tasks (Subsections6.1.3 through 6.1.5) • Section 6.2 presents some widely used wave algorithms. • Section 6.3 considers traversal algorithms • Section 6.4 gives several algorithms for a distributed depth-first search Wave and Traversal Algorithms

  4. Wave and Traversal Algorithms (3) • The treatment of wave algorithms as a separate issue is useful for two reasons. (why study wave algorithm?) • First, the introduction of the concept facilitates the later treatment of more involved algorithms because the properties of their subroutines havealready been studied. • Second, certain problems in distributed computing can be solved by generic constructions that yield a specific algorithm when parameterized with a specific wave algorithm. Wave and Traversal Algorithms

  5. Definition and Use of Wave Algorithms Wave and Traversal Algorithms

  6. Definition of Wave Algorithms (1) Wave and Traversal Algorithms

  7. Definition of Wave Algorithms (2) Wave and Traversal Algorithms

  8. Definition of Wave Algorithms (3) Wave and Traversal Algorithms

  9. Definition of Wave Algorithms (4) Wave and Traversal Algorithms

  10. Definition of Wave Algorithms (5) Wave and Traversal Algorithms

  11. Elementary Results about Wave Algorithms (1) Wave and Traversal Algorithms

  12. Elementary Results about Wave Algorithms (2) Wave and Traversal Algorithms

  13. Elementary Results about Wave Algorithms (3) Wave and Traversal Algorithms

  14. Propagation of Information with Feedback (1) Wave and Traversal Algorithms

  15. Propagation of Information with Feedback (2) Wave and Traversal Algorithms

  16. Synchronization Wave and Traversal Algorithms

  17. Computation of Infimum Functions (1) Wave and Traversal Algorithms

  18. Computation of Infimum Functions (2) Wave and Traversal Algorithms

  19. Computation of Infimum Functions (3) Wave and Traversal Algorithms

  20. A Collection of Wave Algorithms (1) • In all cases the algorithm text is given for theprocess p. • The Ring Algorithm Wave and Traversal Algorithms

  21. A Collection of Wave Algorithms (2) Wave and Traversal Algorithms

  22. A Collection of Wave Algorithms (3) • The Tree Algorithm (when a process receive all messages from its neighbor, decide) Wave and Traversal Algorithms

  23. A Collection of Wave Algorithms (4) (leave to root, root to leave) Wave and Traversal Algorithms

  24. A Collection of Wave Algorithms (5) • The Echo Algorithm Wave and Traversal Algorithms

  25. A Collection of Wave Algorithms (6) Wave and Traversal Algorithms

  26. A Collection of Wave Algorithms (7) • The Polling Algorithm Wave and Traversal Algorithms

  27. A Collection of Wave Algorithms (8) Wave and Traversal Algorithms

  28. A Collection of Wave Algorithms (9) • The Phase Algorithm Wave and Traversal Algorithms

  29. A Collection of Wave Algorithms (10) Wave and Traversal Algorithms

  30. A Collection of Wave Algorithms (11) Wave and Traversal Algorithms

  31. A Collection of Wave Algorithms (12) • Finn's Algorithm Wave and Traversal Algorithms

  32. A Collection of Wave Algorithms (13) Wave and Traversal Algorithms

  33. A Collection of Wave Algorithms (14) Wave and Traversal Algorithms

  34. Traversal Algorithms (1) Wave and Traversal Algorithms

  35. Traversal Algorithms (2) Wave and Traversal Algorithms

  36. Traversal Algorithms (3) • Traversing Cliques Wave and Traversal Algorithms

  37. Traversal Algorithms (4) Wave and Traversal Algorithms

  38. Traversal Algorithms (5) • Traversing Tori Wave and Traversal Algorithms

  39. Traversal Algorithms (6) • Traversing Hypercubes Wave and Traversal Algorithms

  40. Traversal Algorithms (7) • Traversing Connected Networks • A traversal algorithm for arbitrary connected networks was given by Tarry in 1895. Wave and Traversal Algorithms

  41. Wave and Traversal Algorithms

  42. Time Complexity: Depth-first Search (1) • The processes in Tarry's algorithm are given sufficient freedom, in choosing a neighbor to which to forward the token. • In Section 6.4.1, a minor modification of Tarry's algorithm enables the algorithm to compute depth-first search trees. (classical depth-first search algorithm) • In Subsection 6.4.2 two algorithms will be discussed that compute depth-first search trees in less time than the classical algorithm. • In Subsection 6.4.3 a depth-first search algorithm will be presented for networks with initial knowledge of neighbors' identities. Wave and Traversal Algorithms

  43. Time Complexity: Depth-first Search (2) • The time complexity of distributed algorithms Wave and Traversal Algorithms

  44. Distributed Depth-first Search (1) Wave and Traversal Algorithms

  45. Wave and Traversal Algorithms

  46. Depth-first Search Algorith'ms Using Linear Time • Awerbuch's solution • Cidon's solution Wave and Traversal Algorithms

  47. Wave and Traversal Algorithms

  48. Wave and Traversal Algorithms

  49. Wave and Traversal Algorithms

  50. Depth-first Search with Neighbor Knowledge Wave and Traversal Algorithms

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