Integrating and sampling cuts in bounded treewidth graphs

Abstract

In this paper, we consider the problem of evaluating (s, t)-cuts in a bounded treewidth graph. In particular, we show how to compute the partition function for weighted cuts of the graph, i.e., the total weight of all (s, t)-cuts where the weight of a single cut is the product of its edge weights. This method can also easily be adapted to work with additive weights for the cost of a cut. We also present a method for sampling a cut proportional to its weight in linear time. Computing the partition function is #P-hard for general graphs, and our sampling algorithm is simple enough to prove useful is several application areas. Finally, we discuss an alternative method for sampling cuts that uses Markov chains and show that, in the worst case, its mixing time is exponential in the size of the graph even when the graph has bounded treewidth.