Computing branchwidth via efficient triangulations and blocks

Fedor V. Fomin (1) , Frédéric Mazoit (2) , Ioan Todinca (3)

1 UiB - Department of Informatics [Bergen]
2 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166
3 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

Minimal triangulations and potential maximal cliques are the main ingredients for a number of polynomial time algorithms on different graph classes computing the treewidth of a graph. Potential maximal cliques are also the main engine of the fastest so far O(1.9601^n)-time exact treewidth algorithm. Based on the recent results of Mazoit, we define the structures that can be regarded as minimal triangulations and potential maximal cliques for branchwidth: efficient triangulations and blocks. We show how blocks can be used to construct an algorithm computing the branchwidth of a graph on n vertices in time (2+√3)^n · n^O(1).

Mots clés: branchwidth; graph; algorithm

Domaines: Mathématique discrète [cs.DM]

Fedor V. Fomin, Frédéric Mazoit, Ioan Todinca. Computing branchwidth via efficient triangulations and blocks. International Workshop on Graph-Theoretic Concepts in Computer Science, Jun 2005, France. pp.374-384, ⟨10.1007/11604686_33⟩. ⟨hal-00380511⟩