Algorithms for Variable-Weighted 2-SAT and Dual Problems

Abstract. In this paper we study NP-hard weighted satisfiability optimization problems for the class 2-CNF providing worst-case upper time bounds. Moreover we consider the monotone dual class consisting of clause sets where all variables occur at most twice. We show that weighted SAT, XSAT and NAESAT optimization problems for this class are polynomial time solvable using appropriate reductions to specific polynomial time solvable graph problems. Key Words: weighted satisfiability, optimization problem, NP-hardness, edge cover, graph factor, perfect matching

• Type: Conference
• Year: 2007
• Where: SAT
• Authors: Stefan Porschen, Ewald Speckenmeyer
• Keywords: Optimization Problem, SAT 2007, Time Solvable Graph, Weighted Satisfiability Optimization