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 ()
Additional contact information
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, 2021, vol. 42, issue 3, No 11, 524-542

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)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-019-00421-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:42:y:2021:i:3:d:10.1007_s10878-019-00421-1

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-019-00421-1

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().