Gaspers, Serge
[Author];
Gudmundsson, Joachim
[Author];
Jones, Mitchell
[Author];
Mestre, Julián
[Author];
Rümmele, Stefan
[Author]
;
Serge Gaspers and Joachim Gudmundsson and Mitchell Jones and Julián Mestre and Stefan Rümmele
[Contributor]
Footnote:
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Description:
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 treewidth k, 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 quality of the solution.