Counting the number of solutions for instances of satisfiability
Theoretical Computer Science
Characterising tractable constraints
Artificial Intelligence
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Complexity of generalized satisfiability counting problems
Information and Computation
On the hardness of approximate reasoning
Artificial Intelligence
Number of models and satisfiability of sets of clauses
Theoretical Computer Science
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An algorithm for counting maximum weighted independent sets and its applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Constraints and universal algebra
Annals of Mathematics and Artificial Intelligence
Counting Satisfying Assignments in 2-SAT and 3-SAT
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Counting Models Using Connected Components
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Improved Bounds for Sampling Coloring
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
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Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2-SAT instances, where the total number of solutions to these instances is the same as those of the original problem. The algorithm consists of two main cases, depending on whether the domain size d is even, in which case the algorithm runs in O(1.3247n 驴 (d/2)n) time, or odd, in which case it runs in O(1.3247n 驴 ((d2 + d + 2)/4)n/2) if d = 4 驴 k + 1, and O(1.3247n 驴 ((d2 + d)/4)n/2) if d = 4 驴 k + 3. We also give an algorithm for counting the number of possible 3-colourings of a given graph, which runs in O(1.8171n), an improvement over our general algorithm gained by using problem specific knowledge.