Counting the number of solutions to CSP instances has vast applications in several areas ranging from statistical physics to artificial intelligence. We provide a new algorithm for counting the number of solutions to binary CSP s which has a time complexity ranging from O ((d/4 · α4) n) to O ((α + α5 + [d/4 - 1] · α4)n) (where α ≈ 1.2561) depending on the domain size d ≥ 3. This is substantially faster than previous algorithms, especially for small d. We also provide an algorithm for counting k-colourings in graphs and its running time ranges from O (⌊log2 k⌋n) to O(⌊log;2 k + 1⌋n) depending on k ≥ 4. Previously, only an O (1.8171n) time algorithm for counting 3-colourings were known, and we improve this upper bound to O (1.7879n). © Springer-Verlag 2003.
CITATION STYLE
Angelsmark, O., & Jonsson, P. (2003). Improved algorithms for counting solutions in constraint satisfaction problems. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2833, 81–95. https://doi.org/10.1007/978-3-540-45193-8_6
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