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
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Algorithms finding tree-decompositions of graphs
Journal of Algorithms
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
The nonexistence of reduction rules giving an embedding into a k-tree
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
On Linear Recognition of Tree-Width at Most Four
SIAM Journal on Discrete Mathematics
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Pre-processing for Triangulation of Probabilistic Networks
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
On the maximum cardinality search lower bound for treewidth
Discrete Applied Mathematics
Fast recommendations using GAI models
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Weighted treewidth algorithmic techniques and results
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Decision making with multiple objectives using GAI networks
Artificial Intelligence
A branch and bound algorithm for exact, upper, and lower bounds on treewidth
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Degree-Based treewidth lower bounds
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
On the maximum cardinality search lower bound for treewidth
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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Several sets of reductions rules are known for preprocessing a graph when computing its treewidth. In this paper, we give reduction rules for a weighted variant of treewidth, motivated by the analysis of algorithms for probabilistic networks. We present two general reduction rules that are safe for weighted treewidth, which generalise many of the existing reduction rules for treewidth. Experimental results show that these reduction rules can significantly reduce the problem size for several instances of real-life probabilistic networks.