Minimum Size Tree-Decompositions

2 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We study in this paper the problem of computing a tree-decomposition of a graph with width at most k and minimum number of bags. More precisely, we focus on the following problem: given a fixed $k ≥ 1$, what is the complexity of computing a tree-decomposition of width at most k with minimum number of bags in the class of graphs with treewidth at most k? We prove that the problem is NP-complete for any fixed $k ≥$4 and polynomial for $k ≤ 2$; for $k = 3$, we show that it is polynomial in the class of trees and 2-connected outerplanar graphs.
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Article dans une revue
Discrete Applied Mathematics, Elsevier, 2017, 〈10.1016/j.dam.2017.01.030〉

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https://hal.inria.fr/hal-01620389
Contributeur : Nicolas Nisse <>
Soumis le : jeudi 23 novembre 2017 - 15:26:18
Dernière modification le : lundi 5 novembre 2018 - 15:36:03

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MSTD-DAM-v3.pdf
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Bi Li, Fatima Zahra Moataz, Nicolas Nisse, Karol Suchan. Minimum Size Tree-Decompositions. Discrete Applied Mathematics, Elsevier, 2017, 〈10.1016/j.dam.2017.01.030〉. 〈hal-01620389〉

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