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

We present a new algorithm, called LB-Triang, which computes minimal triangulations. We give both a straightforward O(nm0) 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 signi cantly di erent from other existing triangulation techniques. We examine several interesting and useful properties of this algorithm, and give some experimental results. 1 Background and motivation Computing a triangulation consists in embedding a given graph into a triangulate...

• Type: Journal
• Year: 2006
• Where: JAL
• Authors: Anne Berry, Jean Paul Bordat, Pinar Heggernes, Geneviève Simonet, Yngve Villanger
• Keywords: Chordal Graph, JAL 2006, Minimal Triangulation, Triangulation