A Single-Exponential Time 2-Approximation Algorithm for Treewidth

  title={A Single-Exponential Time 2-Approximation Algorithm for Treewidth},
  author={Tuukka Korhonen},
  journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)},
  • T. Korhonen
  • Published 15 April 2021
  • Computer Science
  • 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
We give an algorithm, that given an n-vertex graph <tex>$G$</tex> and an integer k, in time 2<sup>O(k)</sup>n either outputs a tree decomposition of <tex>$G$</tex> of width at most 2k + 1 or determines that the treewidth of <tex>$G$</tex> 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<sup>O(k)</sup>n and the previous… 

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