Abstract
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be “1” and the other literals in the same clause are set to “0”. If we restrict the length of each clause to be at most 3 literals, then it is known as the X3SAT problem. In this paper, we consider the problem of counting the number of satisfying assignments to the X3SAT problem, which is also known as #X3SAT.
The current state of the art exact algorithm to solve #X3SAT is given by Dahllöf, Jonsson and Beigel and runs in \(O(1.1487^n)\) time, where n is the number of variables in the formula. In this paper, we propose an exact algorithm for the #X3SAT problem that runs in \(O(1.1120^n)\) time with very few branching cases to consider, by using a result from Monien and Preis to give us a bisection width for graphs with at most degree 3.
Sanjay Jain and Frank Stephan are supported in part by the Singapore Ministry of Education Tier 2 grant AcRF MOE2019-T2-2-121/R146-000-304-112. Further, Sanjay Jain is supported in part by NUS grant number C252-000-087-001. We thank the anonymous referees of CP2020 for several helpful comments. An extended technical report is available at https://arxiv.org/pdf/2007.07553.pdf.
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Hoi, G., Jain, S., Stephan, F. (2020). A Faster Exact Algorithm to Count X3SAT Solutions. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_22
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