Chordal completions of planar graphs
Journal of Combinatorial Theory Series B
On treewidth and minimum fill-in of asteroidal triple-free graphs
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Obtaining highly accurate topology estimates of evolutionary trees from very short sequences
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
A wide-range efficient algorithm for minimal triangulation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
A practical algorithm for making filled graphs minimal
Theoretical Computer Science
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
SIAM Journal on Matrix Analysis and Applications
Recognizing weakly triangulated graphs by edge separability
Nordic Journal of Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
How to Use the Minimal Separators of a Graph for its Chordal Triangulation
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Minimal Elimination Ordering Inside a Given Chordal Graph
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Efficient Implementation of a Minimal Triangulation Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Theoretical Computer Science
Discrete Applied Mathematics
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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.