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Exact (Exponential) Algorithms for Treewidth and Minimum Fill-In

  • Fedor V. Fomin
  • Dieter Kratsch
  • Ioan Todinca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

We show that for a graph G on n vertices its treewidth and minimum fill-in can be computed roughly in 1.9601 n time. Our result is based on a combinatorial proof that the number of minimal separators in a graph is \(\mathcal O(n \cdot 1.7087^n)\) and that the number of potential maximal cliques s is \(\mathcal O(n^4 \cdot 1.9601^n)\).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Dieter Kratsch
    • 2
  • Ioan Todinca
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.LITAUniversité de MetzMetz Cedex 01France
  3. 3.LIFOUniversité d’OrléansOrléans Cedex 2France

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