## Abstract

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 language | English (US) |
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Pages (from-to) | 116-135 |

Number of pages | 20 |

Journal | Algorithmica |

Volume | 80 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2018 |

## Keywords

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

## ASJC Scopus subject areas

- General Computer Science
- Computer Science Applications
- Applied Mathematics