Computing Branchwidth Via Efficient Triangulations and Blocks

  • Fedor Fomin
  • Frédéric Mazoit
  • Ioan Todinca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3787)


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 \(\mathcal{O}\)(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 + \(\sqrt{\rm 3}\))\(^{\it n}\) · n O(1).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Fedor Fomin
    • 1
  • Frédéric Mazoit
    • 2
  • Ioan Todinca
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.LIFUniversité de provenceMarseilleFrance
  3. 3.LIFOUniversité d’OrléansOrléansFrance

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