Turbocharging Treewidth Heuristics
- 40 Downloads
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-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.
KeywordsTree decomposition Heuristic Fixed-parameter tractability Local search
We thank Michael R. Fellows for inspiring this line of research.
- 6.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)Google Scholar
- 7.Gaspers, S., Gudmundsson, J., Jones, M., Mestre, J., Rümmele, S.: Turbocharging treewidth heuristics. In: Guo, J., Hermelin, D. (eds.) 11th International Symposium on Parameterized and Exact Computation, IPEC 2016, LIPIcs, vol. 63, pp. 13:1–13:13 (2016)Google Scholar
- 8.Gaspers, S., Gudmundsson, J., Jones, M., Mestre, J., Rümmele, S.: Turbocharging treewidth heuristics (2016). https://github.com/mfjones/pace2016. Accessed 4 Aug 2018
- 9.Gogate, V., Dechter, R.: A complete anytime algorithm for treewidth. In: Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 201–208. AUAI Press (2004)Google Scholar