A ck n 5-Approximation Algorithm for Treewidth

@article{Bodlaender2016ACN,
  title={A ck n 5-Approximation Algorithm for Treewidth},
  author={Hans L. Bodlaender and P{\aa}l Gr{\o}n{\aa}s Drange and Markus S. Dregi and Fedor V. Fomin and Daniel Lokshtanov and Michal Pilipczuk},
  journal={SIAM J. Comput.},
  year={2016},
  volume={45},
  pages={317-378}
}
We give an algorithm that for an input n-vertex graph G and integer k > 0, in time 2n 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… CONTINUE READING

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