Dynamic programming for H-minor-free graphs

Juanjo Rué, Ignasi Sau, Dimitrios M. Thilikos

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)86-97
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7434 LNCS
StatePublished - 2012
Event18th Annual International Computing and Combinatorics Conference, COCOON 2012 - Sydney, NSW, Australia
Duration: Aug 20 2012Aug 22 2012


  • analysis of algorithms
  • branchwidth
  • dynamic programming
  • graphs minors
  • non-crossing partitions
  • parameterized algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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