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Chordless Paths Through Three Vertices

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Parameterized and Exact Computation (IWPEC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3162))

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Abstract

Consider the following problem, that we call “Chordless Path through Three Vertices” or Cp3v, for short: Given a simple undirected graph G=(V,E), a positive integer k, and three distinct vertices s, t, and v∈ V, is there a chordless path from s via v to t in G that consists of at most k vertices? In a chordless path, no two vertices are connected by an edge that is not in the path. Alternatively, one could say that the subgraph induced by the vertex set of the path in G is the path itself. The problem has been raised in the context of service deployment in communication networks. We resolve the parametric complexity of Cp3v by proving it W[1]-complete with respect to its natural parameter k. Our reduction extends to a number of related problems about chordless paths. In particular, deciding on the existence of a single directed chordless (s,t)-path in a digraph is also W[1]-complete with respect to the length of the path.

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Author information

Authors and Affiliations

  1. IBM Zurich Research Laboratory, Rüschlikon

    Robert Haas

  2. Institute for Theoretical Computer Science, ETH Zürich,  

    Michael Hoffmann

Authors
  1. Robert Haas
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  2. Michael Hoffmann
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Editor information

Editors and Affiliations

  1. School of Mathematics, Statistics, and Computer Science, Victoria University, PO Box 600, Wellington, New Zealand

    Rod Downey

  2. PCRU, Office of DVC (Research), University of Newcastle, Australia

    Michael Fellows

  3. Carleton University, Ottawa, Canada

    Frank Dehne

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Haas, R., Hoffmann, M. (2004). Chordless Paths Through Three Vertices. In: Downey, R., Fellows, M., Dehne, F. (eds) Parameterized and Exact Computation. IWPEC 2004. Lecture Notes in Computer Science, vol 3162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28639-4_3

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  • DOI: https://doi.org/10.1007/978-3-540-28639-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23071-7

  • Online ISBN: 978-3-540-28639-4

  • eBook Packages: Springer Book Archive

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