Optimal decomposition by clique separators
Discrete Mathematics
Enumerating all connected maximal common subgraphs in two graphs
Theoretical Computer Science
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
Optimal decomposition of belief networks
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Target-Oriented Branch and Bound Method for Global Optimization
Journal of Global Optimization
Finding All Maximal Cliques in Dynamic Graphs
Computational Optimization and Applications
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
Note: A note on the problem of reporting maximal cliques
Theoretical Computer Science
Modeling and Reasoning with Bayesian Networks
Modeling and Reasoning with Bayesian Networks
Triangulation Heuristics for BN2O Networks
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Best-first search for treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
A practical algorithm for finding optimal triangulations
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
Approximate Common Intervals in Multiple Genome Comparison
BIBM '11 Proceedings of the 2011 IEEE International Conference on Bioinformatics and Biomedicine
On the tree structure used by lazy propagation for inference in bayesian networks
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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To perform efficient inference in Bayesian networks by means of a Junction Tree method, the network graph needs to be triangulated. The quality of this triangulation largely determines the efficiency of the subsequent inference, but the triangulation problem is unfortunately NP-hard. It is common for existing methods to use the treewidth criterion for optimality of a triangulation. However, this criterion may lead to a somewhat harder inference problem than the total table size criterion. We therefore investigate new methods for depth-first search and best-first search for finding optimal total table size triangulations. The search methods are made faster by efficient dynamic maintenance of the cliques of a graph. This problem was investigated by Stix, and in this paper we derive a new simple method based on the Bron-Kerbosch algorithm that compares favourably to Stix' approach. The new approach is generic in the sense that it can be used with other algorithms than just Bron-Kerbosch. The algorithms for finding optimal triangulations are mainly supposed to be off-line methods, but they may form the basis for efficient any-time heuristics. Furthermore, the methods make it possible to evaluate the quality of heuristics precisely and allow us to discover parts of the search space that are most important to direct randomized sampling to.