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

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. © 2004 Elsevier Inc. All rights reserved.