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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Bibliographic Details
Published in:	Algorithmica Vol. 84; no. 4; pp. 982 - 1006
Main Authors:	Li, Wenjun, Xu, Chao, Yang, Yongjie, Chen, Jianer, Wang, Jianxin
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2022 Springer Nature B.V
Subjects:	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
Online Access:	Get full text
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Summary:	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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-022-00938-8