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An FPT 2-Approximation for Tree-cut Decomposition

Kim, Eun Jung; Oum, Sang-Il; Paul, Christophe; Sau Valls, Ignasi; Thilikos, Dimitrios M. (2015), An FPT 2-Approximation for Tree-cut Decomposition, in Sanità, Laura; Skutella, Martin, Approximation and Online Algorithms, Springer : Berlin Heidelberg, p. 35-46. 10.1007/978-3-319-28684-6_4

Type
Communication / Conférence
External document link
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01264015
Date
2015
Conference title
Approximation and Online Algorithms 13th International Workshop, WAOA 2015
Conference date
2015-09
Conference city
Patras
Conference country
Greece
Book title
Approximation and Online Algorithms
Book author
Sanità, Laura; Skutella, Martin
Publisher
Springer
Published in
Berlin Heidelberg
ISBN
978-3-319-28683-9
Pages
35-46
Publication identifier
10.1007/978-3-319-28684-6_4
Metadata
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Author(s)
Kim, Eun Jung
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Oum, Sang-Il

Paul, Christophe

Sau Valls, Ignasi cc

Thilikos, Dimitrios M. cc
Abstract (EN)
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.
Subjects / Keywords
Fixed-parameter tractable algorithm; Tree-cut width; Approximation algorithm

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