Computing branchwidth via efficient triangulations and blocks

Authors:
Fedor V. Fomin;Frédéric Mazoit;Ioan Todinca
Affiliations:
Department of Informatics, University of Bergen, PO Box 7800, 5020 Bergen, Norway;LaBRI Université Bordeaux F-33405 Talence cedex, France;LIFO Université d'Orléans 45067 Orléans cedex 2, France
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

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, exact (exponential) 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 (23)^n@?n^O^(^1^).