Distributed Algorithms on Graphs

Distributed Algorithms on Graphs

Eli Gafni
Nicola Santoro
Copyright Date: 1986
Pages: 200
https://www.jstor.org/stable/j.ctt9qf47j
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  • Book Info
    Distributed Algorithms on Graphs
    Book Description:

    This volume contains papers presented at the First International Workshop on Distributed Algorithms.

    eISBN: 978-0-7735-7347-5
    Subjects: Technology

Table of Contents

  1. Front Matter
    (pp. [i]-[vi])
  2. PREFACE
    (pp. [vii]-[x])
    Eli Gafni and Nicola Santoro
  3. Table of Contents
    (pp. [xi]-2)
  4. 1. THE BIT COMPLEXITY OF PROBABILISTIC LEADER ELECTION ON A UNIDIRECTIONAL RING
    (pp. 3-12)
    Karl Abrahamson, Andrew Adler, Rachel Gelbart, Lisa Higham and David Kirkpatrick

    This paper is concerned with the problem of leader election on an asynchronous, unidirectional ring ofnprocessors. The specific goal is to study the inherent complexity of leader election under various additional assumptions about the ring, where the complexity is considered to be the average number ofbitstransmitted on the ring.

    The results of this paper strengthen a number of the bounds proved by Itai and Rodeh [IR] who pioneered the study of probabilistic algorithms for leader election in unidirectional rings. Itai and Rodeh point out that if the processors on the ring are identical, probabilistic techniques must...

  5. 2. MINIMIZING A VIRTUAL CONTROL TOKEN RING
    (pp. 13-26)
    Sven Arne Andreasson

    Virtual control token rings have been proposed as a method of achieving resource allocation and synchronization in distributed systems using mesh networks for interprocess communication [LeLann 77]. This virtual ring can also be used to find an extrema value among nodes, The Circular Extrema Problem [Peters 82].

    A unique capability, a control token, is passed among the different computer sites (nodes) and only the site that is in possession of the control token is allowed to take that action which the token controls, e.g. a file update. The token is dedicated to some resources and their locks are contained in...

  6. 3. NEW UPPERBOUNDS FOR DECENTRALIZED EXTREMA-FINDING IN A RING OF PROCESSORS
    (pp. 27-40)
    H. L. Bodlaender and J. van Leeuwen

    Consider n processors connected in a network, and distinguished by unique identification numbers. Every processor only has local information about the network topology, viz. it only knows the processors to which it is connected through a direct link. In a number of distributed algorithms it is required that the active processors elect a central coordinator (a "leader"), e.g. as part of an initialisation or restart procedure. The problem arises to design a protocol by means of which any active processor can incite the election and every processor will learn the identification number of the leader in as small a number...

  7. 4. EFFICIENT ALGORITHMS FOR ROUTING INFORMATION IN A MULTICOMPUTER SYSTEM
    (pp. 41-48)
    Zvi Drezner and Amnon Barak

    In this paper we analyze algorithms for routing information between the nodes of a multicomputer, which consists of a large set of independent computers that are interconnect by a local area communication network. These algorithms are useful when it is desired to reduce the number of messages and the time delay necessary to transmit information from any node to the other nodes of the multicomputer. Two types of routing algorithms are discussed. In the first case, we assume a deterministic routing, i.e, each node sends messages to a fixed set of prespecified nodes. The second algorithm is based on messages...

  8. 5. LOWER BOUNDS ON COMMON KNOWLEDGE IN DISTRIBUTED ALGORITHMS
    (pp. 49-68)
    Eliezer Gafni, Michael C. Loui, Prasoon Tiwari, Douglas B. West and Shmuel Zaks

    An algorithm for a distributed computer system achievescommon knowledgeif it computes a function that requires the participation of all processors. Korachet al. (1984) call such a functionglobal. The processors compute this global function by exchanging some local information at each step.

    Efficient distributed algorithms have been designed to compute maxima (Dolevet al., 1982; Peterson, 1982), medians (Frederickson, 1983; Rodeh, 1982; Santoro and Sidney, 1982), minimum spanning trees (Gallageret al., 1983), shortest paths (Chandy and Misra, 1982), and maximum flows (Segall, 1982). Each of these algorithms achieves common knowledge.

    In this paper we study further...

  9. 6. SCHEME FOR EFFICIENCY-PERFORMANCE MEASURES OF DISTRIBUTED AND PARALLEL ALGORITHMS
    (pp. 69-102)
    Ivan Lavallée and Christian Lavault

    The emergence of parallel machines with great abilities to parallel computing as well as large distributed networks require other conceptions in the design and analysis of algorithms. Under the term of "parallelism" itself actually subsumes a varied flourishing reality. "Parallel computers" are often meant to be parallel machines (SIMD or MIMD type, synchronous or asynchronous, data or control-flow, etc…) as well as distributed networks, although the algorithmic background is essentially different with regard to data structures. Global data are allowed in the classical parallel case, whereas in essence distributed systems only allowlocal data. As far as the complexity measures...

  10. 8. DUPLICATE ROUTING IN DISTRIBUTED NETWORKS
    (pp. 103-114)
    Ariel Orda and Raphael Rom

    In some computer networks or internetworks a phenomenon of packet loss takes place. This loss can be due to a node or link becoming inoperative, in which caseallpackets passing through that node or link are lost. Another cause of packet loss may be statistical. For example, gateways in an internetwork may destroy packets at will [1,2,3] in which case not all packets passing through that node are destroyed. This paper addresses packet loss of the second kind.

    We propose an approach to increase network reliability by allowing nodes to duplicate packets. Duplication is not limited to the source...

  11. 9. NOTES ON DISTRIBUTED ALGORITHMS IN UNIDIRECTIONAL RINGS
    (pp. 115-122)
    Jan Pachl and Doron Rotem

    This paper offers some opinions related to, and conclusions extracted from, a detailed study of the number of messages needed to find the maximum label in any unidirectional asynchronous ring of labeled processes. The basic approach and most results are taken from [7] and [8].

    A number of labeled processes are connected by communication channels to form a unidirectional ring. Initially, each process knows only its own label (which is unique in the ring). Processes may communicate only by messages sent along the communication channels.

    The communication isasynchronous, in the sense that messages may be arbitrarily delayed in the...

  12. 10. SENSE OF DIRECTION AND COMMUNICATION COMPLEXITY IN DISTRIBUTED NETWORKS
    (pp. 123-132)
    Nicola Santoro, Jorge Urrutia and Shmuel Zaks

    Consider a network ofnprocessors. Each processor has a distinct identity of which it alone is aware, and has available some labeled direct communication lines to other (possibly, all) processors; it also knows the (non-negative) cost associated with each such line. The network can viewed as an undirected graph G=(V,E) where |V|=n. Communication is achieved by sending messages along the communication lines. It is assumed that messages arrive, with no error, after a finite but otherwise arbitrary delay, and are kept in order of arrival in a queue until processed. All processors execute the same algorithm, which involves local...

  13. 11. THE COMMUNICATIONS COMPLEXITY HIERARCHY IN DISTRIBUTED COMPUTING
    (pp. 133-142)
    J. B. Sidney and J. Urrutia

    Since the pioneering research of Cook [1] and Karp [3] in computational complexity, an enormous amount of research has been directed toward establishing the position of problems in the complexity hierarchy: polynomial, weakly NP-complete, strongly NP-complete, etc. In rough terms, the computational complexity of a problem is an asymptotic measure of the "amount of time" needed to solve all instances of a problem using a finite state Turing machine with an infinitely long tape. The complexity hierarchy as currently understood depends for its existence on the assumption that P ≠ NP, i.e., that there are problems solvable in exponential time...

  14. 12. SIMULATION OF CHAOTIC ALGORITHMS BY TOKEN ALGORITHMS
    (pp. 143-152)
    Prasoon Tiwari and Michael C. Loui

    A distributed computer system comprises processors connected by an asynchronous communication network. In a distributed algorithm, many processors may transmit messages at the same time. An algorithm ischaoticif each processor may transmit whenever it has a message to send. For example, the algorithm of Gallageret al. (1983) is chaotic.

    In contrast, in atokenalgorithm, at any time ony the processor that holds the token can pass it on to one of its neighbors. For example, many local networks implement only token algorithms (Tanenbaum, 1981; Stallings, 1984), and Gafni and Afek (1984) give a token algorithm. Token...

  15. 13. A GENERAL DISTRIBUTED GRAPH ALGORITHM FOR FAIR ACCESS TO CRITICAL SECTIONS
    (pp. 153-160)
    Horst F. Wedde

    We deal with the following problems:

    Given an arbitrary undirected graph where each node is understood to represent a sequential process. Each such process has just onecritical section, and two neighbors cannot use their critical sections but mutually exclusively. Direct communication between neighbors may occur in both directions, even simultaneously.

    There is no way to establish any kind of centralized control. No assumption on relative speeds, on fixed priorities, on shared memory etc. is allowed.

    An algorithm has then to be designed which does not deadlock and which is fair in the sense that any node process when interested...

  16. OPEN PROBLEMS
    (pp. 163-164)
  17. A BIBLIOGRAPHY OF DISTRIBUTED ALGORITHMS (1985)
    (pp. 165-188)
    Nicola Santoro
  18. AUTHOR INDEX
    (pp. 189-190)