Arc and path consistence revisited
Artificial Intelligence
Dempster's rule of combination is #P-complete (research note)
Artificial Intelligence
On the hardness of approximate reasoning
Artificial Intelligence
Probabilistic Arc Consistency: A Connection between Constraint Reasoning and Probabilistic Reasoning
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Complete Solving of Linear Diophantine Equations and Inequations without Adding Variables
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
Towards a Dichotomy Theorem for the Counting Constraint Satisfaction Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
The good old Davis-Putnam procedure helps counting models
Journal of Artificial Intelligence Research
Discrete Applied Mathematics
Guiding Search using Constraint-level Advice
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Quantifying privacy in multiagent planning
Multiagent and Grid Systems - Planning in multiagent systems
Solution counting algorithms for constraint-centered search heuristics
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Counting solutions of knapsack constraints
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Exploiting problem structure for solution counting
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Counting homomorphisms via hypergraph-based structural restrictions
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Counting-based search: branching heuristics for constraint satisfaction problems
Journal of Artificial Intelligence Research
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Determining the number of solutions of a CSP has several applications in AI, in statistical physics, and in guiding backtrack search heuristics. It is a #P-complete problem for which some exact and approximate algorithms have been designed. Successful CSP models often use high-arity, global constraints to capture the structure of a problem. This paper exploits such structure and derives polytime evaluations of the number of solutions of individual constraints. These may be combined to approximate the total number of solutions or used to guide search heuristics. We give algorithms for several of the main families of constraints and discuss the possible uses of such solution counts.