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arXiv · 1304.6321

A O(c^k n) 5-Approximation Algorithm for Treewidth

Hans Bodlaender·Pål G. Drange·Markus S. Dregi·Fedor V. Fomin·Daniel Lokshtanov·Michał Pilipczuk
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Abstract

We give an algorithm that for an input n-vertex graph G and integer k>0, in time 2^[O(k)]n either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k+4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single-exponential in k and linear in n. Treewidth based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single-exponential in the treewidth and linear in the input size.

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Hans Bodlaender, Pål G. Drange, Markus S. Dregi, Fedor V. Fomin, Daniel Lokshtanov, Michał Pilipczuk. 2013-04-23. A O(c^k n) 5-Approximation Algorithm for Treewidth. https://arxiv.org/abs/1304.6321

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