  We show how to find a minimum weight loop cutset in a Bayesian network with
high probability. Finding such a loop cutset is the first step in the method of
conditioning for inference. Our randomized algorithm for finding a loop cutset
outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least
1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is
the minimal size of a minimum weight loop cutset, and n is the number of
vertices. We also show empirically that a variant of this algorithm often finds
a loop cutset that is closer to the minimum weight loop cutset than the ones
found by the best deterministic algorithms known.
