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We show how to find a small loop curser 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 andarXiv:1302.6787v1 fatcat:jeb6elksozg4boinlntigsqj5u