## 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 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 language | English (US) |
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Pages (from-to) | 86-97 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 7434 LNCS |

DOIs | |

State | Published - 2012 |

Event | 18th Annual International Computing and Combinatorics Conference, COCOON 2012 - Sydney, NSW, Australia Duration: Aug 20 2012 → Aug 22 2012 |

## Keywords

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

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science