A New Lower Bound for Tree-Width Using Maximum Cardinality Search
Brian Lucena · SIAM Journal on Discrete Mathematics · 2003
The tree-width of a graph is of great importance in applied problems in graphical models. The complexity of inference problems on Markov random fields is exponential in the tree-width of the graph. However, computing tree-width is NP-hard in general. Easily computable upper bounds exist, but there are few lower bounds. We give a novel technique to compute a lower bound for the tree-width of a graph using maximum cardinality search. This bound is efficiently computable and is guaranteed to do at least as well as finding the largest clique in the graph.