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Formal language constrained path problems

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Algorithm Theory — SWAT'98 (SWAT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1432))

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Abstract

Given an alphabet σ, a (directed) graph G whose edges are weighted and σ-labeled, and a formal language L \(\subseteq\) σ*, we consider the problem of finding a shortest (simple) path p in G complying with the additional constraint that l(p) ∃ L. Here l(p) denotes the unique word given by concatenating the σ-labels in G along the path p.

We consider the computational complexity of the problem for different classes of formal languages (finite, regular, context free and context sensitive), different classes of graphs (unrestricted, grids, treewidth bounded) and different type of path (shortest and shortest simple).

A number of variants of the problem are considered and both polynomial time algorithms as well as hardness results (NP-, PSPACE-hardness) are obtained. The hardness and the polynomial time algorithms presented here are a step towards finding such classes of graphs for which polynomial time query evaluation is possible.

Research supported by the Department of Energy under Contract W-7405-ENG-36.

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Authors and Affiliations

  1. Los Alamos National Laboratory, P.O. Box 1663, MS M997, 87545, Los Alamos, NM

    Chris Barrett, Riko Jacob & Madhav Marathe

Authors
  1. Chris Barrett
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  2. Riko Jacob
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  3. Madhav Marathe
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Stefan Arnborg Lars Ivansson

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© 1998 Springer-Verlag Berlin Heidelberg

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Barrett, C., Jacob, R., Marathe, M. (1998). Formal language constrained path problems. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054371

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  • DOI: https://doi.org/10.1007/BFb0054371

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64682-2

  • Online ISBN: 978-3-540-69106-8

  • eBook Packages: Springer Book Archive

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