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![Page 1: 2015/11/17Wave and Traversal Algorithms1 Introduction to Distributed Algorithm Part Two: Fundamental Algorithm Chapter 6- Wave and Traversal Algorithms.](https://reader035.fdocuments.net/reader035/viewer/2022062722/56649f295503460f94c433ed/html5/thumbnails/1.jpg)
112/04/20Wave and Traversal
Algorithms 1
Introduction to Distributed AlgorithmPart Two: Fundamental Algorithm
Chapter 6- Wave and Traversal Algorithms
Teacher: Chun-Yuan Lin
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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)
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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 (Subsections 6.1.3 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
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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 have already 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.
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Algorithms 5
Definition and Use of Wave Algorithms
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Algorithms 6
Definition of Wave Algorithms (1)
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Algorithms 7
Definition of Wave Algorithms (2)
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Algorithms 8
Definition of Wave Algorithms (3)
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Algorithms 9
Definition of Wave Algorithms (4)
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Algorithms 10
Definition of Wave Algorithms (5)
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Algorithms 11
Elementary Results about Wave Algorithms (1)
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Algorithms 12
Elementary Results about Wave Algorithms (2)
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Algorithms 13
Elementary Results about Wave Algorithms (3)
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Algorithms 14
Propagation of Information with Feedback (1)
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Algorithms 15
Propagation of Information with Feedback (2)
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Algorithms 16
Synchronization
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Algorithms 17
Computation of Infimum Functions (1)
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Algorithms 18
Computation of Infimum Functions (2)
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Algorithms 19
Computation of Infimum Functions (3)
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Algorithms 20
A Collection of Wave Algorithms (1)
In all cases the algorithm text is given for the process p.
The Ring Algorithm
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Algorithms 21
A Collection of Wave Algorithms (2)
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Algorithms 22
A Collection of Wave Algorithms (3) The Tree Algorithm
(when a process receive all messages from its neighbor, decide)
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Algorithms 23
A Collection of Wave Algorithms (4)
(leave to root, root to leave)
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Algorithms 24
A Collection of Wave Algorithms (5) The Echo Algorithm
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Algorithms 25
A Collection of Wave Algorithms (6)
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Algorithms 26
A Collection of Wave Algorithms (7) The Polling Algorithm
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Algorithms 27
A Collection of Wave Algorithms (8)
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Algorithms 28
A Collection of Wave Algorithms (9) The Phase Algorithm
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Algorithms 29
A Collection of Wave Algorithms (10)
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Algorithms 30
A Collection of Wave Algorithms (11)
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Algorithms 31
A Collection of Wave Algorithms (12)
Finn's Algorithm
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Algorithms 32
A Collection of Wave Algorithms (13)
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Algorithms 33
A Collection of Wave Algorithms (14)
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Algorithms 34
Traversal Algorithms (1)
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Algorithms 35
Traversal Algorithms (2)
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Algorithms 36
Traversal Algorithms (3) Traversing Cliques
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Algorithms 37
Traversal Algorithms (4)
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Algorithms 38
Traversal Algorithms (5) Traversing Tori
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Algorithms 39
Traversal Algorithms (6) Traversing Hypercubes
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Algorithms 40
Traversal Algorithms (7) Traversing Connected Networks
A traversal algorithm for arbitrary connected networks was given by Tarry in 1895.
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Algorithms 41
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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.
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Algorithms 43
Time Complexity: Depth-first Search (2)
The time complexity of distributed algorithms
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Algorithms 44
Distributed Depth-first Search (1)
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Algorithms 45
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Algorithms 46
Depth-first Search Algorith'ms Using Linear Time
Awerbuch's solution
Cidon's solution
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Algorithms 47
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Algorithms 48
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Algorithms 49
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Algorithms 50
Depth-first Search with Neighbor Knowledge
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Algorithms 51
Remaining Issues (1) Overview of Wave Algorithms
Computing Sums Impossibility of a general construction Computing the sum with a traversal algorithm Computing the sum using a spanning tree Computing the sum using identities
Alternative Definitions of Time Complexity
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Algorithms 52
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Algorithms 53
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Algorithms 54
Remaining Issues (2)
Definitions based on more restrictive timing assumptions
Definition based on message chains