Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Characterization and recognition of partial 3-trees
SIAM Journal on Algebraic and Discrete Methods
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Easy problems for tree-decomposable graphs
Journal of Algorithms
A linear time algorithm for finding tree-decompositions of small treewidth
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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
Finding All Minimal Separators of a Graph
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
A sufficiently fast algorithm for finding close to optimal junction trees
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Bucket elimination: a unifying framework for probabilistic inference
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Learning Markov networks: maximum bounded tree-width graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Maximum likelihood bounded tree-width Markov networks
Artificial Intelligence
Optimizing exact genetic linkage computations
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
Node deletion sequences in influence diagrams using genetic algorithms
Statistics and Computing
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Tree decomposition and discrete optimization problems: A survey
Cybernetics and Systems Analysis
On a generalization of triangulated graphs for domains decomposition of CSPs
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
Treewidth computations I. Upper bounds
Information and Computation
Generation of tree decompositions by iterated local search
EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
Treewidth computations II. Lower bounds
Information and Computation
SPOOK: a system for probabilistic object-oriented knowledge representation
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Pre-processing for triangulation of probabilistic networks
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
New upper bound heuristics for treewidth
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Exploiting the probability of observation for efficient bayesian network inference
Canadian AI'12 Proceedings of the 25th Canadian conference on Advances in Artificial Intelligence
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
All roads lead to Rome---New search methods for the optimal triangulation problem
International Journal of Approximate Reasoning
Evaluating tree-decomposition based algorithms for answer set programming
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
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An algorithm called QUICKTREE is developed for finding a triangulation T of a given undirected graph G such that the size of T's maximal clique is minimum and such that no other triangulation of G is a subgraph of T. We have tested QUICKTREE on graphs of up to 100 nodes for which the maximum clique in an optimal triangulation is of size 11. This is the first algorithm that can optimally triangulate graphs of such size in a reasonable time frame. This algorithm is useful for constraint satisfaction problems and for Bayesian inference through the clique tree inference algorithm.