, Volume 81, Issue 2, pp 439–475 | Cite as

Turbocharging Treewidth Heuristics

  • Serge Gaspers
  • Joachim Gudmundsson
  • Mitchell Jones
  • Julián Mestre
  • Stefan RümmeleEmail author


A widely used class of algorithms for computing tree decompositions of graphs are heuristics that compute an elimination order, i.e., a permutation of the vertex set. In this paper, we propose to turbocharge these heuristics. For a target treewidthk, suppose the heuristic has already computed a partial elimination order of width at most k, but extending it by one more vertex exceeds the target width k. At this moment of regret, we solve a subproblem which is to recompute the last c positions of the partial elimination order such that it can be extended without exceeding width k. We show that this subproblem is fixed-parameter tractable when parameterized by k and c, but it is para-NP-hard and W[1]-hard when parameterized by only k or c, respectively. Our experimental evaluation of the FPT algorithm shows that we can trade a reasonable increase of the running time for the quality of the solution.


Tree decomposition Heuristic Fixed-parameter tractability Local search 



We thank Michael R. Fellows for inspiring this line of research.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.UNSW SydneySydneyAustralia
  2. 2.Data61, CSIROCanberraAustralia
  3. 3.University of SydneyCamperdownAustralia
  4. 4.University of Illinois at Urbana-ChampaignChampaignUSA

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