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Algorithmica

, Volume 36, Issue 4, pp 375–408 | Cite as

Computing the Treewidth and the Minimum Fill-In with the Modular Decomposition

  • Hans L. Bodlaender
  • Udi Rotics
Article

Abstract

Using the notion of modular decomposition we extend the class of graphs on which both the treewidth and the minimum fill-in can be solved in polynomial time. We show that if C is a class of graphs that are modularly decomposable into graphs that have a polynomial number of minimal separators, or graphs formed by adding a matching between two cliques, then both the treewidth and the minimum fill-in on C can be solved in polynomial time. For the graphs that are modular decomposable into cycles we give algorithms that use respectively O(n) and O(n3) time for treewidth and minimum fill-in.

Keywords

Treewidth Minimum fill-in Modular decomposition Minimal separators Polynomial algorithms Graph algorithms 

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Copyright information

© Springer-Verlag New York 2003

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Udi Rotics
    • 2
  1. 1.Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands. hansb@cs.uu.nl.NL
  2. 2.School of Mathematics and Computer Science, Netanya Academic College, P.O. Box 120, 42100 Netanya, Israel. rotics@mars.netanya.ac.il.IL

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