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Article Dans Une Revue Theoretical Computer Science Année : 2013

Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems

Binh-Minh Bui-Xuan
Jan Arne Telle
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Martin Vatshelle
  • Fonction : Auteur

Résumé

Given a graph $G$ we provide dynamic programming algorithms for many locally checkable vertex subset and vertex partitioning problems. Their runtime is polynomial in the number of equivalence classes of problem-specific equivalence relations on subsets of vertices, defined on a given decomposition tree of $G$. Using these algorithms all these problems become solvable in polynomial time for many well-known graph classes like interval graphs and permutation graphs (Belmonte and Vatshelle (2013)). Given a decomposition of boolean-width $k$ we show that the algorithms will have runtime $O(n^{4}2^{O(k^{2})})$, providing the first large class of problems solvable in fixed-parameter single-exponential time in boolean-width.

Dates et versions

hal-01146167 , version 1 (27-04-2015)

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Binh-Minh Bui-Xuan, Jan Arne Telle, Martin Vatshelle. Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems. Theoretical Computer Science, 2013, 511, pp.66-76. ⟨10.1016/j.tcs.2013.01.009⟩. ⟨hal-01146167⟩
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