An FPT 2-Approximation for Tree-Cut Decomposition

Eun Jung Kim (1) , Sang-Il Oum (2) , Christophe Paul (3) , Ignasi Sau (3) , Dimitrios M. Thilikos (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 Department of Mathematical Sciences, KAIST
3 ALGCO - Algorithmes, Graphes et Combinatoire

The tree-cut width of a graph is a graph parameter defined by Wollan (J Combin 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.

Mots clés: Multiway Cut; Digraph homomorphism; approximation algorithm; Parameterized complexity; Fixed-Parameter Tractable algorithm; tree-cut width

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Eun Jung Kim, Sang-Il Oum, Christophe Paul, Ignasi Sau, Dimitrios M. Thilikos. An FPT 2-Approximation for Tree-Cut Decomposition. Algorithmica, 2018, 80 (1), pp.116-135. ⟨10.1007/s00453-016-0245-5⟩. ⟨hal-01690385⟩