1. An FPT 2-Approximation for Tree-Cut Decomposition.
- Author
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Kim, Eun, Oum, Sang-il, Paul, Christophe, Sau, Ignasi, and Thilikos, Dimitrios
- Subjects
MATHEMATICAL optimization ,MATHEMATICAL decomposition ,PARAMETERS (Statistics) ,ALGORITHMS ,APPROXIMATION algorithms - 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 2 w, in time $$2^{O(w^2\log w)} \cdot n^2$$ . 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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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