An FPT 2-Approximation for Tree-Cut Decomposition

Abstract : The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47-66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequate than treewidth as an invariant that, when bounded, can accelerate the resolution of intractable problems. While designing algorithms for problems with bounded tree-cut width, it is important to have a parametrically tractable way to compute the exact value of this parameter or, at least, some constant approximation of it. In this paper we give a parameterized 2-approximation algorithm for the computation of tree-cut width; for an input n-vertex graph G and an integer w, our algorithm either confirms that the tree-cut width of G is more than w or returns a tree-cut decomposition of G certifying that its tree-cut width is at most 2w, in time 2O(w2logw)⋅n2. Prior to this work, no constructive parameterized algorithms, even approximated ones, existed for computing the tree-cut width of a graph. As a consequence of the Graph Minors series by Robertson and Seymour, only the existence of a decision algorithm was known.
Type de document :
[Research Report] LIRMM. 2015
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Contributeur : Dimitrios M. Thilikos <>
Soumis le : vendredi 6 novembre 2015 - 12:14:03
Dernière modification le : jeudi 11 janvier 2018 - 06:26:13


  • HAL Id : lirmm-01225569, version 1
  • ARXIV : 1509.04880



Eunjung Kim, Sang-Il Oum, Christophe Paul, Ignasi Sau, Dimitrios M. Thilikos. An FPT 2-Approximation for Tree-Cut Decomposition. [Research Report] LIRMM. 2015. 〈lirmm-01225569〉



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