A Solution for the Processor Allocation Problem: Topology Conserving Graph Mapping by Self-Organization

  • M. Dormanns
  • H.-U. Heiss


We consider the problem of how to allocate the tasks of a parallel program to the processor elements of a multicomputer system such that the communication overhead of the program is minimized. This problem basically amounts to a graph embedding problem since both the program and the multicomputer can be modeled as graphs. The embedding problem can be characterized as the search for a topology conserving mapping of the source graph to the target graph.

To find such mappings we apply the Kohonen selforganization process. Our main concern in this article is to show how this graph embedding problem can be fitted to the Kohonen technique. To that end, we introduce feature vectors for each node of the source graph to provide topological information exceeding direct neighborhood and considering larger surroundings.

The particular optimization goal of the task mapping problem is being related to known results of the Kohonen process. The behavior and performance of our approach is illustrated by some sample graphs.


Feature Vector Communication Cost Parallel Program Topological Information Target Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Heiss H-U, ‘Classification of Problems and Algorithms for Processor Allocation in Parallel Systems’, Internal Report 7/91, University of Karlsruhe, 1991.Google Scholar
  2. [2]
    Neuhaus P, ‘Solving the Mapping-Problem — Experiences with a Genetic Algorithm’, Parallel Problem Solving from Nature 1990, Proceedings, Springer LNCS 496, pp. 170-175.Google Scholar
  3. [3]
    Bollinger S W and Midkiff S F, ‘Heuristic Technique for Processor and Link Assignment in Multicomputers’, IEEE Trans. on Computers, Vol. 40, No. 3, pp. 325–333, March 1991.CrossRefGoogle Scholar
  4. [4]
    Mühlenbein H, Gorges-Schleuter M and Krämer O, ‘New solutions to the mapping problem of parallel systems: The evolution approach’, Parallel Computing 4, pp. 269–279, 1987.Google Scholar
  5. [5]
    Hemani A and Postula A, ‘Cell Placement by Self-Organization’, Neural Networks, Vol. 3, pp. 377–383, 1990.CrossRefGoogle Scholar
  6. [6]
    Ritter H, Martinetz T and Schulten K, ‘Neural Networks’, Addison Wesley 1991.Google Scholar

Copyright information

© Springer-Verlag/Wien 1993

Authors and Affiliations

  • M. Dormanns
    • 1
  • H.-U. Heiss
    • 1
  1. 1.Department of InformaticsUniversity of KarlsruheKarlsruhe 1Germany

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