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Paths of Bounded Length and Their Cuts: Parameterized Complexity and Algorithms

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Parameterized and Exact Computation (IWPEC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5917))

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Abstract

We study the parameterized complexity of two families of problems: the bounded length disjoint paths problem and the bounded length cut problem. From Menger’s theorem both problems are equivalent (and computationally easy) in the unbounded case for single source, single target paths. However, in the bounded case, they are combinatorially distinct and are both NP-hard, even to approximate. Our results indicate that a more refined landscape appears when we study these problems with respect to their parameterized complexity. For this, we consider several parameterizations (with respect to the maximum length l of paths, the number k of paths or the size of a cut, and the treewidth of the input graph) of all variants of both problems (edge/vertex-disjoint paths or cuts, directed/undirected). We provide FPT-algorithms (for all variants) when parameterized by both k and l and hardness results when the parameter is only one of k and l. Our results indicate that the bounded length disjoint-path variants are structurally harder than their bounded length cut counterparts. Also, it appears that the edge variants are harder than their vertex-disjoint counterparts when parameterized by the treewidth of the input graph.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Petr A. Golovach

  2. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, GR15784, Athens, Greece

    Dimitrios M. Thilikos

Authors
  1. Petr A. Golovach
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  2. Dimitrios M. Thilikos
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Editors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA

    Jianer Chen

  2. Institutt for informatikk, Universitetet i Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

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Golovach, P.A., Thilikos, D.M. (2009). Paths of Bounded Length and Their Cuts: Parameterized Complexity and Algorithms. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_17

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  • DOI: https://doi.org/10.1007/978-3-642-11269-0_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11268-3

  • Online ISBN: 978-3-642-11269-0

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