Faster computation of path-width

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    6 Citations (Scopus)

    Abstract

    Tree-width and path-width are widely successful concepts.Many NP-hard problems have efficient solutions when restricted to graphs of bounded tree-width.Many efficient algorithms are based on a tree decomposition.Sometimes the more restricted path decomposition is required.The bottleneck for such algorithms is often the computation of the width and a corresponding tree or path decomposition.For graphs with n vertices and tree-width or path-width k, the standard linear time algorithm to compute these decompositions dates back to 1996.Its running time is linear in n and exponential in k3 and not usable in practice.Here we present a more efficient algorithm to compute the path-width and provide a path decomposition.Its running time is 2O(k2)n.In the classical algorithm of Bodlaender and Kloks, the path decomposition is computed from a tree decomposition.Here, an optimal path decomposition is computed from a path decomposition of about twice the width.The latter is computed from a constant factor smaller graph.

    Original languageEnglish (US)
    Title of host publicationCombinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings
    EditorsVeli Mäkinen, Simon J. Puglisi, Leena Salmela
    PublisherSpringer Verlag
    Pages385-396
    Number of pages12
    ISBN (Print)9783319445427
    DOIs
    StatePublished - Jan 1 2016
    Event27th International Workshop on Combinatorial Algorithms, IWOCA 2016 - Helsinki, Finland
    Duration: Aug 17 2016Aug 19 2016

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9843 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other27th International Workshop on Combinatorial Algorithms, IWOCA 2016
    CountryFinland
    CityHelsinki
    Period8/17/168/19/16

    Fingerprint

    Path Decomposition
    Pathwidth
    Decomposition
    Tree Decomposition
    Treewidth
    Efficient Algorithms
    Graph in graph theory
    Bounded Treewidth
    Optimal Path
    Linear-time Algorithm
    NP-hard Problems
    Efficient Solution
    Date
    Decompose
    Computational complexity

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Furer, M. (2016). Faster computation of path-width. In V. Mäkinen, S. J. Puglisi, & L. Salmela (Eds.), Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings (pp. 385-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-44543-4_30
    Furer, Martin. / Faster computation of path-width. Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. editor / Veli Mäkinen ; Simon J. Puglisi ; Leena Salmela. Springer Verlag, 2016. pp. 385-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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    title = "Faster computation of path-width",
    abstract = "Tree-width and path-width are widely successful concepts.Many NP-hard problems have efficient solutions when restricted to graphs of bounded tree-width.Many efficient algorithms are based on a tree decomposition.Sometimes the more restricted path decomposition is required.The bottleneck for such algorithms is often the computation of the width and a corresponding tree or path decomposition.For graphs with n vertices and tree-width or path-width k, the standard linear time algorithm to compute these decompositions dates back to 1996.Its running time is linear in n and exponential in k3 and not usable in practice.Here we present a more efficient algorithm to compute the path-width and provide a path decomposition.Its running time is 2O(k2)n.In the classical algorithm of Bodlaender and Kloks, the path decomposition is computed from a tree decomposition.Here, an optimal path decomposition is computed from a path decomposition of about twice the width.The latter is computed from a constant factor smaller graph.",
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    Furer, M 2016, Faster computation of path-width. in V Mäkinen, SJ Puglisi & L Salmela (eds), Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9843 LNCS, Springer Verlag, pp. 385-396, 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, Helsinki, Finland, 8/17/16. https://doi.org/10.1007/978-3-319-44543-4_30

    Faster computation of path-width. / Furer, Martin.

    Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. ed. / Veli Mäkinen; Simon J. Puglisi; Leena Salmela. Springer Verlag, 2016. p. 385-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9843 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    Furer M. Faster computation of path-width. In Mäkinen V, Puglisi SJ, Salmela L, editors, Combinatorial Algorithms - 27th International Workshop, IWOCA 2016, Proceedings. Springer Verlag. 2016. p. 385-396. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-44543-4_30