We provide a framework for the design and analysis of dynamic programming algorithms for H-minor-free graphs with branchwidth at most k. Our technique applies to a wide family of problems where standard (deterministic) dynamic programming runs in 2 O(k·logk)·n O(1) steps, with n being the number of vertices of the input graph. Extending the approach developed by the same authors for graphs embedded in surfaces, we introduce a new type of branch decomposition for H-minor-free graphs, called an H-minor-free cut decomposition, and we show that they can be constructed in O h(n 3) steps, where the hidden constant depends exclusively on H. We show that the separators of such decompositions have connected packings whose behavior can be described in terms of a combinatorial object called ℓ-triangulation. Our main result is that when applied on H-minor-free cut decompositions, dynamic programming runs in 2 oh(k)·n o(1) steps. This broadens substantially the class of problems that can be solved deterministically in single-exponential time for H-minor-free graphs. © 2012 Springer-Verlag.
CITATION STYLE
Rué, J., Sau, I., & Thilikos, D. M. (2012). Dynamic programming for H-minor-free graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7434 LNCS, pp. 86–97). https://doi.org/10.1007/978-3-642-32241-9_8
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