Abstract
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.
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Notes
We refer the reader who is not familiar with some of these notions to the Preliminaries section.
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Acknowledgements
We thank Michael R. Fellows for inspiring this line of research.
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A preliminary version appeared in the Proceedings of the 11th International Symposium on Parameterized and Exact Computation (IPEC 2016) [7]. Serge Gaspers is the recipient of an Australian Research Council (ARC) Future Fellowship (FT140100048). The authors acknowledge support under the ARC’s Discovery Projects funding scheme (DP150101134 and DP180102870).
Experimental Results
Experimental Results
See Tables 4, 5, 6, 7, 8, 9, 10 and 11.
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Gaspers, S., Gudmundsson, J., Jones, M. et al. Turbocharging Treewidth Heuristics. Algorithmica 81, 439–475 (2019). https://doi.org/10.1007/s00453-018-0499-1
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DOI: https://doi.org/10.1007/s00453-018-0499-1