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

Chao Xu (), Wenjun Li (), Jianxin Wang () and Yongjie Yang ()
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Chao Xu: Central South University
Wenjun Li: Changsha University of Science and Technology
Jianxin Wang: Central South University
Yongjie Yang: Central South University

Journal of Combinatorial Optimization, No 0, 19 pages

Abstract: Abstract We study the $$(n, 3)$$ ( 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 $$(n, 3)$$ ( n , 3 ) -MaxSAT problem which significantly improves the previous results. More precisely, the running time of our algorithm can be bounded by $$O^*(1.175^k)$$ O ∗ ( 1 . 175 k ) and $$O^*(1.194^n)$$ O ∗ ( 1 . 194 n ) , respectively. Prior to our study, the running time of the best known exact algorithm can be bounded by $$O^*(1.194^k)$$ O ∗ ( 1 . 194 k ) and $$O^*(1.237^n)$$ O ∗ ( 1 . 237 n ) , respectively.

Keywords: CNF formula; 3-SAT; Branching algorithm; Complexity; Parameterized complexity (search for similar items in EconPapers)
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DOI: 10.1007/s10878-019-00421-1

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