Modular-Width: An Auxiliary Parameter for Parameterized Parallel Complexity

  • Faisal N. Abu-Khzam
  • Shouwei Li
  • Christine Markarian
  • Friedhelm Meyer auf der Heide
  • Pavel Podlipyan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)

Abstract

Many graph problems such as maximum cut, chromatic number, hamiltonian cycle, and edge dominating set are known to be fixed-parameter tractable (FPT) when parameterized by the treewidth of the input graphs, but become W-hard with respect to the clique-width parameter. Recently, Gajarský et al. proposed a new parameter called modular-width using the notion of modular decomposition of graphs. They showed that the chromatic number problem and the partitioning into paths problem, and hence hamiltonian path and hamiltonian cycle, are FPT when parameterized by this parameter. In this paper, we study modular-width in parameterized parallel complexity and show that the weighted maximum clique problem and the maximum matching problem are fixed-parameter parallel-tractable (FPPT) when parameterized by this parameter.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Faisal N. Abu-Khzam
    • 1
    • 4
  • Shouwei Li
    • 2
  • Christine Markarian
    • 3
  • Friedhelm Meyer auf der Heide
    • 2
  • Pavel Podlipyan
    • 2
  1. 1.Department of Computer Science and MathematicsLebanese American UniversityBeirutLebanon
  2. 2.Heinz Nixdorf Institute and Department of Computer SciencePaderborn UniversityPaderbornGermany
  3. 3.Department of Mathematical SciencesHaigazian UniversityBeirutLebanon
  4. 4.School of Engineering and Information TechnologyCharles Darwin UniversityDarwinAustralia

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