A Refined Branching Algorithm for the Maximum Satisfiability Problem

The Maximum satisfiability problem ( MaxSAT ) is a fundamental NP-hard problem which has significant applications in many areas. Based on refined observations, we derive a branching algorithm of running time  O ∗ ( 1 . 2989 m ) for the MaxSAT problem, where  m denotes the number of clauses in the gi...

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Veröffentlicht in:Algorithmica Jg. 84; H. 4; S. 982 - 1006
Hauptverfasser: Li, Wenjun, Xu, Chao, Yang, Yongjie, Chen, Jianer, Wang, Jianxin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2022
Springer Nature B.V
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Polynomials
Theory of Computation
Maximum satisfiability
Branching algorithms
Exact algorithms
ISSN:0178-4617, 1432-0541
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Zusammenfassung:The Maximum satisfiability problem ( MaxSAT ) is a fundamental NP-hard problem which has significant applications in many areas. Based on refined observations, we derive a branching algorithm of running time  O ∗ ( 1 . 2989 m ) for the MaxSAT problem, where  m denotes the number of clauses in the given CNF formula. Our algorithm considerably improves the previous best result  O ∗ ( 1 . 3248 m ) published in 2004. For our purpose, we derive improved branching strategies for variables of degrees 3, 4, and 5. The worst case of our branching algorithm is at certain degree-4 variables. To serve the branching rules, we also propose a variety of reduction rules which can be exhaustively applied in polynomial time.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00938-8