A primal–dual approximation algorithm for Minsat

We characterize the optimal solution to the linear programming relaxation of the standard formulation for the minimum satisfiability problem. We give a O(nm2) combinatorial algorithm to solve the fractional version of the minimum satisfiability problem optimally where n(m) is the number of variables...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 319; pp. 372 - 381
Main Authors: Arif, Umair, Benkoczi, Robert, Gaur, Daya Ram, Krishnamurti, Ramesh
Format: Journal Article
Language:English
Published: Elsevier B.V 15.10.2022
Subjects:
Minimum satisfiability
Primal–dual schema
Primal–dual schema
Minimum satisfiability
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:We characterize the optimal solution to the linear programming relaxation of the standard formulation for the minimum satisfiability problem. We give a O(nm2) combinatorial algorithm to solve the fractional version of the minimum satisfiability problem optimally where n(m) is the number of variables (clauses). As a by-product, we obtain a 2(1−1∕2k) approximation algorithm for the minimum satisfiability problem where k is the maximum number of literals in any clause.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2021.07.016