A New Lower Bound for Tree-Width Using Maximum Cardinality Search

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 treewidth 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.