Abstract
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 
time, or odd, in which case it runs in 
if d = 4 · k + 1, and 
if d = 4 · k + 3. We also give an algorithm for counting the number of possible 3-colourings of a given graph, which runs in 
, an improvement over our general algorithm gained by using problem specific knowledge.
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Angelsmark, O., Jonsson, P., Linusson, S., Thapper, J. (2002). Determining the Number of Solutions to Binary CSP Instances. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_22
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DOI: https://doi.org/10.1007/3-540-46135-3_22
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