Weighted Treewidth: Algorithmic Techniques and Results

Abstract

From the analysis of algorithms for probabilistic networks, it is known that a tree decomposition of the minimum treewidth may not be optimal for these algorithms. Instead of treewidth, we consider therefore the weighted treewidth of a weighted graph. In this paper, we present a number of heuristics for determining upper and lower bounds on the weighted treewidth, and a branch and bound algorithm for finding the exact weighted treewidth for weighted graphs.