An FPT 2-approximation for tree-cut decomposition

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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(w2 log w) ・ 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.
Publisher
Springer Verlag
Issue Date
2015-09
Language
English
Citation

13th International Workshop on Approximation and Online Algorithms, WAOA 2015, pp.35 - 46

ISSN
0302-9743
DOI
10.1007/978-3-319-28684-6_4
URI
http://hdl.handle.net/10203/314525
Appears in Collection
MA-Conference Papers(학술회의논문)
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