We give an algorithm, which 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  ]  .
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) 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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. 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)
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FOCS 2013, SICOMP 2016
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. Our algorithm is based on a local improvement method adapted from a proof of Bellenbaum and Diestel
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Comb. Probab. Comput. 2002