# Dynamic Programming for $H$-minor-free Graphs

2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : 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 2Oh(k)⋅nO(1) steps. This broadens substantially the class of problems that can be solved deterministically in single-exponential time for H-minor-free graphs.
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Conference papers

Cited literature [35 references]

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00736708
Contributor : Ignasi Sau <>
Submitted on : Friday, September 20, 2019 - 1:12:47 PM
Last modification on : Tuesday, January 14, 2020 - 1:36:09 PM

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### Citation

Juanjo Rué, Ignasi Sau Valls, Dimitrios M. Thilikos. Dynamic Programming for $H$-minor-free Graphs. COCOON: Computing and Combinatorics Conference, Aug 2012, Sydney, NSW, Australia. pp.86-97, ⟨10.1007/978-3-642-32241-9_8⟩. ⟨lirmm-00736708⟩

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