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

Binh-Minh Bui-Xuan 1 Jan Arne Telle Martin Vatshelle 
1 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : 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.
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Submitted on : Monday, April 27, 2015 - 5:52:23 PM
Last modification on : Sunday, June 26, 2022 - 9:43:54 AM

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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, Elsevier, 2013, 511, pp.66-76. ⟨10.1016/j.tcs.2013.01.009⟩. ⟨hal-01146167⟩

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