Approximate resolution of hard numbering problems

Authors:
Olivier Bailleux;Jean-Jacques Chabrier
Affiliations:
CRID Université de Bourgogne, Faculté des Sciences Mirande, Dijon Cedex, France;CRID Université de Bourgogne, Faculté des Sciences Mirande, Dijon Cedex, France
Venue:
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Year:
1996

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Abstract

We present a new method for estimating the number of solutions of constraint satisfaction problems. We use a stochastic forward checking algorithm for drawing a sample of paths from a search tree. With this sample, we compute two values related to the number of solutions of a CSP instance. First, an unbiased estimate, second, a lower bound with an arbitrary low error probability. We will describe applications to the Boolean Satisfiability problem and the Queens problem. We shall give some experimental results for these problems.