A wide-range algorithm for minimal triangulation from an arbitrary ordering

  • Authors:

  • Anne Berry;Jean-Paul Bordat;Pinar Heggernes;Geneviève Simonet;Yngve Villanger

  • Affiliations:

  • LIMOS UMR CNRS 6158, Ensemble Scientifique des Cézeaux, Université Blaise Pascal, F-63 170 Aubière, France;LIRMM, 161 Rue Ada, F-34392 Montpellier, France;Department of Informatics, University of Bergen, N-5020 Bergen, Norway;LIRMM, 161 Rue Ada, F-34392 Montpellier, France;Department of Informatics, University of Bergen, N-5020 Bergen, Norway

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2006

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Abstract

We present a new algorithm, called LB-Triang, which computes minimal triangulations. We give both a straightforward O(nm^') time implementation and a more involved O(nm) time implementation, thus matching the best known algorithms for this problem. Our algorithm is based on a process by Lekkerkerker and Boland for recognizing chordal graphs which checks in an arbitrary order whether the minimal separators contained in each vertex neighborhood are cliques. LB-Triang checks each vertex for this property and adds edges whenever necessary to make each vertex obey this property. As the vertices can be processed in any order, LB-Triang is able to compute any minimal triangulation of a given graph, which makes it significantly different from other existing triangulation techniques. We examine several interesting and useful properties of this algorithm, and give some experimental results.