Approximation Algorithms for the Loop Cutset Problem

We show how to find a small loop cutset in a Bayesian network. Finding such a loop cutset is the first step in the method of conditioning for inference. Our algorithm for finding a loop cutset, called MGA, finds a loop cutset which is guaranteed in the worst case to contain less than twice the number of variables contained in a minimum loop cutset. We test MGA on randomly generated graphs and find that the average ratio between the number of instances associated with the algorithms ' output and the number of instances associated with a minimum solution is 1.22. 1 Introduction Most inference algorithms for the computation of a posterior probability in general Bayesian networks have two conceptual phases. One phase handles operations on the graphical structure itself and the other performs probabilistic computations. For example, the clique tree algorithm requires us to first find a "good" clique tree and then perform probabilistic computations on the clique tree [LS88]. Pearl's method ..