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

Author

Listed:
  • Chao Xu

    (Central South University)

  • Wenjun Li

    (Changsha University of Science and Technology)

  • Jianxin Wang

    (Central South University)

  • Yongjie Yang

    (Central South University
    Saarland University)

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.

Suggested Citation

  • Chao Xu & Wenjun Li & Jianxin Wang & Yongjie Yang, 0. "An improved algorithm for the $$(n, 3)$$ ( n , 3 ) -MaxSAT problem: asking branchings to satisfy the clauses," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-19.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-019-00421-1
    DOI: 10.1007/s10878-019-00421-1
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