Random Algorithms for the Loop Cutset Problem

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 "Repeated WGuessI", outputs a minimum loop cutset, after O(c 6^k k n) steps, with probability at least 1-(1 over{6^k})^{c 6^k}), 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.