TY - JOUR

T1 - Bayes networks for estimating the number of solutions of constraint networks

AU - Meisels, Amnon

AU - Shimony, Solomon Eyal

AU - Solotorevsky, Gadi

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The problem of counting the number of solutions to a constraint network (CN) (also called constraint satisfaction problems, CSPs) is rephrased in terms of probability updating in Bayes networks. Approximating the probabilities in Bayes networks is a problem which has been studied for a while, and may well provide a good approximation to counting the number of solutions. We use a simple approximation based on independence, and show that it is correct for tree-structured CNs. For other CNs, it is less optimistic than a spanning-tree approximation suggested in prior work. Experiments show that the Bayes nets estimation is more accurate on the average, compared to competing methods (the spanning-tree, as well as a scheme based on a product of all compatible pairs of values). We present empirical evidence that our approximation may also be a useful (value ordering) search heuristic for finding a single solution to a constraint satisfaction problem.

AB - The problem of counting the number of solutions to a constraint network (CN) (also called constraint satisfaction problems, CSPs) is rephrased in terms of probability updating in Bayes networks. Approximating the probabilities in Bayes networks is a problem which has been studied for a while, and may well provide a good approximation to counting the number of solutions. We use a simple approximation based on independence, and show that it is correct for tree-structured CNs. For other CNs, it is less optimistic than a spanning-tree approximation suggested in prior work. Experiments show that the Bayes nets estimation is more accurate on the average, compared to competing methods (the spanning-tree, as well as a scheme based on a product of all compatible pairs of values). We present empirical evidence that our approximation may also be a useful (value ordering) search heuristic for finding a single solution to a constraint satisfaction problem.

UR - http://www.scopus.com/inward/record.url?scp=0034365044&partnerID=8YFLogxK

U2 - 10.1023/a:1018956222900

DO - 10.1023/a:1018956222900

M3 - Article

AN - SCOPUS:0034365044

VL - 28

SP - 169

EP - 186

JO - Annals of Mathematics and Artificial Intelligence

JF - Annals of Mathematics and Artificial Intelligence

SN - 1012-2443

IS - 1-4

ER -