Fast Algorithm for Rank-Width
Inspired by the heuristic algorithm for boolean-width by Telle et. al. , we develop a heuristic algorithm for rank-width. We compare results on graphs of practical relevance to the established bounds of boolean-width. While the width of most graphs is lower than the known values for tree-width, it turns out that the boolean-width heuristic is able to find decompositions of significantly lower width. In a second step we therefore present a further algorithm that can decide if for a graph G and a value k exists a rank-decomposition of width lower than k. This enables to show that boolean-width is in fact lower than or equal to rank-width on many of the investigated graphs.
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- 2.Courcelle, B.: The monadic second-order logic of graphs i. recognizable sets of finite graphs. Information and Computation, 12–75 (1990)Google Scholar
- 4.Langer, A., Reidl, F., Rossmanith, P., Sikdar, S.: Recent progress in practical aspects of mso model-checking (in preparation, 2012)Google Scholar
- 6.Hliněny, P., Oum, S.I., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. Computer Journal, 10–1093 (2007)Google Scholar
- 7.Oum, S.I.: Approximating rank-width and clique-width quickly. ACM Trans. Algorithms 5(1), 10:1–10:20 (2008)Google Scholar
- 8.Bodlaender, H., van den Broek, J.W.: Treewidthlib: A benchmark for algorithms for treewidth and related graph problems (2004), http://www.cs.uu.nl/research/projects/treewidthlib/
- 14.Knuth, D.E.: The Stanford GraphBase: a platform for combinatorial computing. ACM, New York (1993)Google Scholar
- 15.Johnson, D.J., Trick, M.A. (eds.): Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993. American Mathematical Society, Boston (1996)Google Scholar
- 17.Rlfap, E., Eindhoven, T.U., Group, R.: Euclid calma radio link frequency assignment project technical annex t-2.3.3: Local search (1995)Google Scholar
- 18.Bilmes, J.: Uai 2006 inference evaluation results. Technical report, University of Washington, Seattle (2006)Google Scholar