Structure, Information and Communication Complexity, IIS 1

Structure, Information and Communication Complexity, IIS 1

Paola Flocchini
Bernard Mans
Nicola Santoro
Copyright Date: 1995
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    Structure, Information and Communication Complexity, IIS 1
    Book Description:

    The ultimate goal of research in Distributed Computing is to understand the nature, properties and limits of computing in a system of autonomous communicating agents. To this end, it is crucial to identify those factors which are significant for the computability and the communication complexity of problems. A crucial role is played by those factors which can be termed Structural Information: its identification, characterization, analysis, and its impact on communication complexity is an important theoretical task which has immediate practical importance. The purpose of the Colloquia on Structural Information and Communication Complexity (SIROCCO) is to focus explicitly on the interaction between structural information and communication complexity. The Colloquia comprise position papers, presentations of current research, and group discussions. Series 1 contains papers presented at the 1st Colloquium on Structural Information and Communication Complexity, held in Ottawa, Canada. Series 2 contains papers presented at the 2nd Colloquium held in Olympia, Greece.

    eISBN: 978-0-7735-9115-8
    Subjects: General Science

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. Preface
    (pp. vii-viii)
  4. Sense of Direction: Formal Definitions and Properties
    (pp. 9-34)
    Paola Flocchini, Bernard Mans and Nicola Santoro

    The ultimate goal of the research inDistributed Computingis to understand the nature, the properties and the limits of computing in a system ofautonomous communicating agents.To this end, it is crucial to identify those factors which are significant for the computability and the communication complexity of problems.

    Adistributed systemis a collection of processing entities (e.g., processors) connected by direct communication links, where each entity has a local nonshared memory and can communicate by sending messages to and receiving messages from its neighbours. Every entity has a distinct label (e.g., port number) associated to each of...

  5. Trade-off between computational power and common knowledge in anonymous rings
    (pp. 35-48)
    Paola Flocchini, Angelo Monti and Alessandro Roncato

    We consider the problem of computing functions in anonymous distributed ring. We assume that each processor has two particular registers, namely a read only input register and a write once output register.The input configuration Iis defined as I=x0x1...xn–1 where xi is the value of the input register (label) of pi. Computation of a functionFonIstarts with input configurationIand ends with each processor having the valueF(I) in its output register.

    The relation between the computational power and the knowledge available to the single processor on the input configuration has been extensively studied...

  6. Orientation of Distributed Networks: Graph- and Group-Theoretic Modelling
    (pp. 49-70)
    Christian Lavault

    One of the main topics under investigation in distributed computing concerns the study and design of network topologies which have optimal efficiency with regard to several specific parameters, such as communication complexity of leader election, spanning tree construction, or broadcasting, ease of routing and message transmission, fault-tolerance, etc. To optimize the communication complexity of distributed algorithms, one introduces labellings on the network links in order to give the networkStructural Information, and more precisely a “Sense of Direction” (or “Orientation”).

    Above all, this paper is a survey on the present “state of the art” in graphtheoretic and group-theoretic modelling of...

  7. Labeled versus Unlabeled Distributed Cayley Networks
    (pp. 71-82)
    Evangelos Kranakis and Danny Krizanc

    One of the main themes of investigation in distributed computation concerns the design of network topologies which have optimal efficiency characteristics with respect to several selected parameters, like complexity of routing and message transmission, fault tolerance, leader election, etc. Many network topologies have been studied in the literature, ranging from rings and meshes to hypercubes and butterflies. To optimize the complexity characteristics of the resulting algorithms one introduces labelings on (a subset of) the underlying network links in order to give the network a sense of direction (or orientation). However, even within such topologies the efficiency of distributed algorithms may...

  8. Classifying Anonymous Networks: When Can Two Networks Compute The Same Set Of Vector-Valued Functions?
    (pp. 83-98)
    Nancy Norris

    A network is a collection of arbitrarily powerful processors connected in some configuration by communication links. This paper addresses two questions about “anonymous networks”, whose processors do not have access to their ids and as a consequence all run the same algorithm during a computation. In anonymous networks the effects of network topology on network behavior are sharply displayed. There are a number of problems; for instance, leader election, which are trivially solvable on non-anonymous networks but whose solvability on an anonymous network depends on the network’s topology. A network with a highly symmetrical graph may not be able, for...

  9. Compact Routing Methods: A Survey
    (pp. 99-110)
    Jan van Leeuwen and Richard B. Tan

    In aparallelcomputer, as more processors are added to increase the computing power, the underlying communication network needs toscalefavorably along with the expansion. As the amount of storage space at each processor is limited, the expansion of the network should not put undue burden locally by requiring excessive space for communication purpose. Theroutingmethods used should also be simple and dynamically adjustable with the growth. The underlying network structure can be quite arbitrary, so the communication methods should not rely on any fixedtopology.More and more emphases are given to this type ofuniversal routing...

  10. Interval Labeling Schemes for Chordal Rings
    (pp. 111-124)
    Michele Flammini, Giorgio Gambosi and Sandro Salomone

    Routing messages between pairs of processors is a fundamental task in a dis tributed network. A network of processors is modeled as an (undirected) connected graphG= (V, E), whereVis a set of n processors andEis a set of pairwise communication links. Assuming some cost function on the network edges exists, it is important to route each message along a shortest path from its source to the destination.

    This can be trivially accomplished by referring, at each nodev,to a complete routing table which specifies, for each destinationu, the set of links incident...

  11. Fault-Tolerant Compact Routing based on Reduced Structural Information in Wormhole-Switching based Networks
    (pp. 125-148)
    Johan Vounckx, G. Deconinck, R. Lauwereins and J. A. Peperstraete

    To meet the ever increasing demand for computational power with the current technology one needs massively parallel computers (MPC) [11]. An MPC consists of thousands of processors working together on the same problem. Its processors are connected together by a communication network over which they exchange information by sending data (messages). Since it is impossible to connect the processors directly, the messages must be routed through the network to reach their destination. Clearly, the routing algorithm needs information about the network structure to route the messages. This information is stored on each node in routing tables. Classical routing tables give,...

  12. The Buffer Potential of a Network
    (pp. 149-150)
    Krzysztof Diks, Evangelos Kranakis, Adam Malinowski and Andrzej Pelc

    In the standard model of anonymous networks [1, 4, 3] it is assumed that each processor is permanently attached to its neighbors in such a way that when a bit arrives the processor knows the neighbor it came from. This is equivalent to assuming that a processor of degree d has d buffers, one corresponding to each neighbor, for storing the bits arriving from respective neighbors. The following question arises: “What network computation can be performed if the number of buffers at a node is less than the degree of the node?”

    This question is considered in [2] for the...

  13. Path Layout in ATM Networks
    (pp. 151-167)
    Oman Gerstel and Shmuel Zaks

    The Asynchronous Transfer Mode (ATM) [19, 5] is the transmission, switching, and multiplexing technique chosen by CCITT for B-ISDN. Due to the future importance of fast, broadband, integrated networks, ATM has been extensively discussed in recent years.

    ATM is based on small fixed size packets, which are calledcells.Because of the very high requirements for switching rates, the routing of the cells must be done by a dedicated hardware, implying very simple routing algorithms. The routing scheme chosen in ATM is based on two fixed labels in the header of each cell (VCI and VPI). These labels serve as...

  14. Back Matter
    (pp. 168-168)