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Optimal parallel shortest paths in small treewidth digraphs

  • Session 1. Chair: Gianfranco Bilardi
  • Conference paper
  • First Online:
Algorithms — ESA '95 (ESA 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 979))

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Abstract

We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give parallel algorithms for the EREW PRAM model of computation that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O(α(n)) time using a single processor, after a preprocessing of O(log2 n) time and O(n) work, where α(n) is the inverse of Ackermann's function. The class of constant treewidth graphs contains outerplanar graphs and series-parallel graphs, among others. To the best of our knowledge, these are the first parallel algorithms which achieve these bounds for any class of graphs except trees. We also give a dynamic algorithm which, after a change in an edge weight, updates our data structures in O(log n) time using O(n α) work, for any constant 0<β< 1. Moreover, we give an algorithm of independent interest: computing a shortest path tree, or finding a negative cycle in O(log2 n) time using O(n) work.

This work was partially supported by the EU ESPRIT Basic Research Action No. 7141 (ALCOM II).

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Shiva Chaudhuri & Christos D. Zaroliagis

Authors
  1. Shiva Chaudhuri
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  2. Christos D. Zaroliagis
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Paul Spirakis

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© 1995 Springer-Verlag Berlin Heidelberg

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Chaudhuri, S., Zaroliagis, C.D. (1995). Optimal parallel shortest paths in small treewidth digraphs. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_132

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  • DOI: https://doi.org/10.1007/3-540-60313-1_132

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60313-9

  • Online ISBN: 978-3-540-44913-3

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