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Tight lower bounds for computing shortest paths on proper interval and bipartite permutation graphs

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Parallel Computing Technologies (PaCT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1277))

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Abstract

Logarithmic time lower bounds for computing the distance between two arbitrary vertices, in a proper interval graph represented by a family of intervals on a real line, and in a bipartite permutation graph represented by a permutation function, on exclusive write PRAM are proved here. The lower bounds are also valid for these classes of graphs represented by adjacency matrices and for their superclasses. Shortest paths on interval and permutation graphs, which, respectively, strictly contain proper interval and bipartite permutation graphs, are known to be computable in logarithmic time on exclusive write PRAM. It follows that the lower bounds derived here are tight.

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Authors and Affiliations

  1. FRL, P. O. Box 18345, 90018, Los Angeles, CA

    Lin Chen

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  1. Lin Chen
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Victor Malyshkin

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© 1997 Springer-Verlag Berlin Heidelberg

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Chen, L. (1997). Tight lower bounds for computing shortest paths on proper interval and bipartite permutation graphs. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 1997. Lecture Notes in Computer Science, vol 1277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63371-5_2

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  • DOI: https://doi.org/10.1007/3-540-63371-5_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63371-6

  • Online ISBN: 978-3-540-69525-7

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