Random Algorithms for the Loop Cutset Problem

Abstract

We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called REPEATEDWGUESSI, out - puts a minimum loop cutset, after O(c.6kkn) steps, with probability at least 1 - (1 - 1/6k)c6k, where c > 1 is a constant specified by the user, k is the size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm, called WRA, often finds a loop cutset that is closer to the minimum loop cutset than the ones found by the best deterministic algorithms known.