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

H.L. Bodlaender, P.G. Drange, M.S. Dregi, F.V. Fomin, D. Lokshtanov, M. Pilipczuk

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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.
Original languageEnglish
Publication statusPublished - 23 Apr 2013
Externally publishedYes


  • cs.DS
  • cs.DM


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