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On complexity of a message-routing strategy for multicomputer systems

  • Multiprocessor Systems And Concurrency
  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 484))

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Abstract

A natural communication problem in a multicomputer system, such as the hypercube, is that a processor (called the source) wants to send a message to a number of other processors (destinations). A message-routing paradigm for such a multidestination communication has been formulated as finding a subgraph called an optimal distance-preserving tree (ODPT). We prove that the problem of finding an ODPT is NP-hard both for the n-cube graph as well as for a graph whose maximum degree is at most three.

The work is supported in part by NSF grant CCR-8903037.

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References

  1. H.-A. Choi, A.-H. Esfahanian, and B. Houck, "Optimal Communication Trees with Application to Hypercube Multicomputers," Proc. 6th Intl. Conf. Theory and Applications of Graph Theory, Kalamazoo, MI, 1988.

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  2. M. R. Garey and D.S. Johnson, Computer and Intractability, W.H. Freeman and Company, San Francisco, 1979.

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  3. Y. Lan, L.M. Ni, and A.-H. Esfahanian, "Relay Approach Message Routing in Hypercube Multiprocessors," Proceedings of the 3rd International Conference on Supercomputing, pp. 174–183, May 1988.

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  4. R.T. Wong, "A Dual Ascent Approach for Steiner Tree Problems on Directed Graphs," Mathematical Programming, Vol. 28, pp. 271–287, 1984.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, George Washington University, 20052, Washington, D.C., USA

    Hyeong-Ah Choi

  2. Computer Science Department, Michigan State University, 48824, E. Lansing, MI, USA

    Abdol-Hossein Esfahanian

Authors
  1. Hyeong-Ah Choi
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  2. Abdol-Hossein Esfahanian
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Rolf H. Möhring

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© 1991 Springer-Verlag Berlin Heidelberg

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Choi, HA., Esfahanian, AH. (1991). On complexity of a message-routing strategy for multicomputer systems. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1990. Lecture Notes in Computer Science, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53832-1_41

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  • DOI: https://doi.org/10.1007/3-540-53832-1_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53832-5

  • Online ISBN: 978-3-540-46310-8

  • eBook Packages: Springer Book Archive

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