A Single-Exponential Time 2-Approximation Algorithm for Treewidth
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We give an algorithm, that given an n-vertex graph G and an integer k, in time 2^O(k) n either outputs a tree decomposition of G of width at most 2k + 1 or determines that the treewidth of G is larger than k. This is the first 2-approximation algorithm for treewidth that is faster than the known exact algorithms. In particular, our algorithm improves upon both the previous best approximation ratio of 5 in time 2^O(k) n and the previous best approximation ratio of 3 in time 2^O(k) n^O(1), both given by Bodlaender et al. [FOCS 2013, SICOMP 2016]. Our algorithm is based on a local improvement method adapted from a proof of Bellenbaum and Diestel [Comb. Probab. Comput. 2002].
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