The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
On the hardness of approximate reasoning
Artificial Intelligence
Graph classes: a survey
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on 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
Optimal decomposition of belief networks
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Weighted hypertree decompositions and optimal query plans
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
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The f-cost of a tree decomposition ({Xi | i 驴 I}, T = (I,F)) for a function f : N 驴 R+ is defined as 驴i驴I f(|Xi|). This measure associates with the running time or memory use of some algorithms that use the tree decomposition. In this paper we investigate the problem to find tree decompositions of minimum f-cost.A function f : N 驴 R+ is fast, if for every i 驴 N: f(i+1) 驴 2 驴 f(i). We show that for fast functions f, every graph G has a tree decomposition of minimum f-cost that corresponds to a minimal triangulation of G; if f is not fast, this does not hold. We give polynomial time algorithms for the problem, assuming f is a fast function, for graphs that has a polynomial number of minimal separators, for graphs of treewidth at most two, and for cographs, and show that the problem is NP-hard for bipartite graphs and for cobipartite graphs.We also discuss results for a weighted variant of the problem derived of an application from probabilistic networks.