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Reconfiguration over Tree Decompositions

  • Amer E. Mouawad
  • Naomi Nishimura
  • Venkatesh Raman
  • Marcin Wrochna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8894)

Abstract

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. The reconfiguration version of a vertex-subset problem \(\textit{Q}\) asks whether it is possible to transform one feasible solution for \(\textit{Q}\) into another in at most \(\ell \) steps, where each step is a vertex addition or deletion, and each intermediate set is also a feasible solution for \(\textit{Q}\) of size bounded by \(k\). Motivated by recent results establishing W[1]-hardness of the reconfiguration versions of most vertex-subset problems parameterized by \(\ell \), we investigate the complexity of such problems restricted to graphs of bounded treewidth. We show that the reconfiguration versions of most vertex-subset problems remain PSPACE-complete on graphs of treewidth at most \(t\) but are fixed-parameter tractable parameterized by \(\ell + t\) for all vertex-subset problems definable in monadic second-order logic (MSOL). To prove the latter result, we introduce a technique which allows us to circumvent cardinality constraints and define reconfiguration problems in MSOL.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Amer E. Mouawad
    • 1
  • Naomi Nishimura
    • 1
  • Venkatesh Raman
    • 2
  • Marcin Wrochna
    • 3
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooOntarioCanada
  2. 2.Institute of Mathematical SciencesChennaiIndia
  3. 3.Institute of Computer ScienceUniwersytet WarszawskiWarsawPoland

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