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A Parameterized Algorithm for Chordal Sandwich

  • Pinar Heggernes
  • Federico Mancini
  • Jesper Nederlof
  • Yngve Villanger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6078)

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.

Keywords

Vertex Cover Maximal Clique Input Graph Tree Decomposition Chordal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pinar Heggernes
    • 1
  • Federico Mancini
    • 1
  • Jesper Nederlof
    • 1
  • Yngve Villanger
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway

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