2020/07/15 by Gordon Hoi, Sanjay Jain, Hoi, Gordon +3
Computer Science · #68Q25 #68W40 #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2007.07553
openalex publication_date 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(1.1487n), 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(1.1120n) 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.