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The Complexity of Some Basic Problems for Dynamic Process Graphs

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Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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Abstract

A fundamental problem in programming multiprocessors is scheduling elementary tasks on the available hardware efficiently. Traditionally, one represents tasks and precedence constraints by a data-flow graph. This representation requires that the set of tasks is known beforehand. Such an approach is not appropriate in situations where the set of tasks is not known exactly in advance, for example, when different options how to continue a program are possible. In this paper dynamic process graph (DPG) will be used to represent the set of all possible executions of a given program. An important feature of this model is that graphs are encoded in a very succinct way. The encoded executions are directed acyclic graphs with a “regular” structure that is typical for parallel programs.

With respect to such a graph representation we investigate the computational complexity of some basic graph-theoretic problems like e.g. what is the minimum depth of a graph represented by a DPG? or what is the size of a subgraph induced by a given node v? In this paper the complexities of these problems are determined precisely. As a consequence approximations of the computational complexity of some variants of scheduling problems are obtained.

Supported by DFG research grant RE 672/3.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, Med. Universität zu Lübeck, Germany

    Andreas Jakoby & Maciej Liśkiewicz

  2. Instytut Informatyki, Uniwersytet Wroclawski, Germany

    Maciej Liśkiewicz

Authors
  1. Andreas Jakoby
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  2. Maciej Liśkiewicz
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Jakoby, A., Liśkiewicz, M. (2001). The Complexity of Some Basic Problems for Dynamic Process Graphs. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_48

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  • DOI: https://doi.org/10.1007/3-540-45678-3_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

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