An improved algorithm for the \((n, 3)\)-MaxSAT problem: asking branchings to satisfy the clauses

  • Chao Xu
  • Wenjun Li
  • Jianxin Wang
  • Yongjie YangEmail author


We study the \((n, 3)\)-MaxSAT problem where we are given an integer k and a CNF formula with n variables, each of which appears in at most 3 clauses, and the question is whether there is an assignment that satisfies at least k clauses. Based on refined observations, we propose a branching algorithm for the \((n, 3)\)-MaxSAT problem which significantly improves the previous results. More precisely, the running time of our algorithm can be bounded by \(O^*(1.175^k)\) and \(O^*(1.194^n)\), respectively. Prior to our study, the running time of the best known exact algorithm can be bounded by \(O^*(1.194^k)\) and \(O^*(1.237^n)\), respectively.


CNF formula 3-SAT Branching algorithm Complexity Parameterized complexity 



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Authors and Affiliations

  1. 1.School of Computer Science and EngineeringCentral South UniversityChangshaChina
  2. 2.Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on TransportationChangsha University of Science and TechnologyChangshaChina
  3. 3.Chair of Economic TheorySaarland UniversitySaarbrückenGermany

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