An FPT 2-Approximation for Tree-Cut Decomposition

Eun Jung Kim, Sang il Oum, Christophe Paul, Ignasi Sau, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)116-135
Number of pages20
Issue number1
StatePublished - Jan 1 2018


  • Approximation algorithm
  • Fixed-parameter tractable algorithm
  • Tree-cut width

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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