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Avoiding matrix multiplication

  • Graph Algorithms And Complexity
  • Conference paper
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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

The fastest known algorithms for many problems on graphs use matrix multiplication as a sub-routine. Some examples of problems solved using matrix multiplication are recognition of transitive graphs, computing the transitive closure of a directed acyclic graph, and finding the neighborhood containment matrix of a graph. In this paper, we show how to avoid using matrix multiplication for these problems on special classes of graphs. This leads to efficient algorithms for recognizing chordal comparability graphs and trapezoid graphs, computing the transitive closure of two dimensional partial orders, and a number of other problems.

We gratefully acknowledge the support of the Vanderbilt University Research Council

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Authors and Affiliations

  1. Dept. of Computer Science, Vanderbilt U., 37235, Nashville, TN

    Tze-Heng Ma & Jeremy P. Spinrad

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  1. Tze-Heng Ma
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  2. Jeremy P. Spinrad
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Rolf H. Möhring

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© 1991 Springer-Verlag Berlin Heidelberg

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Ma, TH., Spinrad, J.P. (1991). Avoiding matrix multiplication. 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_31

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  • DOI: https://doi.org/10.1007/3-540-53832-1_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53832-5

  • Online ISBN: 978-3-540-46310-8

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