Efficient Implementation of a Minimal Triangulation Algorithm

Authors:
Pinar Heggernes;Yngve Villanger
Affiliations:
-;-
Venue:
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Year:
2002

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Abstract

LB-triang, an algorithm for computing minimal triangulations of graphs, was presented by Berry in 1999 [1], and it gave a new characterization of minimal triangulations. The time complexity was conjectured to be O(nm), but this has remained unproven until our result. In this paper we present and prove an O(nm) time implementation of LB-triang, and we call the resulting algorithm LB-treedec. The data structure used to achieve this time bound is tree decomposition. We also report from practical runtime tests on randomly generated graphs which indicate that the expected behavior is even better than the proven bound.