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A Parameterized Algorithm for Chordal Sandwich

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Algorithms and Complexity (CIAC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6078))

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Abstract

Given an arbitrary graph G = (V,E) and an additional set of admissible edges F, the Chordal Sandwich problem asks whether there exists a chordal graph (V,E ∪ F′) such that F′ ⊆ F. This problem arises from perfect phylogeny in evolution and from sparse matrix computations in numerical analysis, and it generalizes the widely studied problems of completions and deletions of arbitrary graphs into chordal graphs. As many related problems, Chordal Sandwich is NP-complete. In this paper we show that the problem becomes tractable when parameterized with a suitable natural measure on the set of admissible edges F. In particular, we give an algorithm with running time \(\mathcal{O}(2^{k}n^{5})\) to solve this problem, where k is the size of a minimum vertex cover of the graph (V, F). Hence we show that the problem is fixed parameter tractable when parameterized by k. Note that the parameter does not assume any restriction on the input graph, and it concerns only the additional edge set F.

This work is supported by the Research Council of Norway.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Pinar Heggernes, Federico Mancini, Jesper Nederlof & Yngve Villanger

Authors
  1. Pinar Heggernes
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  2. Federico Mancini
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  3. Jesper Nederlof
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  4. Yngve Villanger
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Sapienza University of Rome, Via Salaria 113, 00198, Rome, Italy

    Tiziana Calamoneri

  2. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega 240, Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Josep Diaz

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Heggernes, P., Mancini, F., Nederlof, J., Villanger, Y. (2010). A Parameterized Algorithm for Chordal Sandwich . In: Calamoneri, T., Diaz, J. (eds) Algorithms and Complexity. CIAC 2010. Lecture Notes in Computer Science, vol 6078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13073-1_12

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  • DOI: https://doi.org/10.1007/978-3-642-13073-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13072-4

  • Online ISBN: 978-3-642-13073-1

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