Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
New upper bounds for maximum satisfiability
Journal of Algorithms
Approximation algorithms
A logical approach to efficient Max-SAT solving
Artificial Intelligence
Solving (Weighted) Partial MaxSAT through Satisfiability Testing
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Relaxed DPLL Search for MaxSAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Exploiting Cycle Structures in Max-SAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Generalizing Core-Guided Max-SAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Algorithms for Weighted Boolean Optimization
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
New inference rules for Max-SAT
Journal of Artificial Intelligence Research
MINIMAXSAT: an efficient weighted max-SAT solver
Journal of Artificial Intelligence Research
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Resolution in Max-SAT and its relation to local consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
MaxSolver: An efficient exact algorithm for (weighted) maximum satisfiability
Artificial Intelligence
UBCSAT: an implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
A complete calculus for Max-SAT
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Solving MAXSAT by solving a sequence of simpler SAT instances
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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MAXSAT is an optimization version of SAT capable of expressing a variety of practical problems. MAXSAT solvers have been designed to take advantage of many of the successful techniques of SAT solvers. However, the most important technique of modern SAT solvers, clause learning, has not been utilized since learnt clauses cannot be soundly added to a MAXSAT theory. In this paper we present a new method that allows SAT clause learning to be exploited in a MAXSAT solver without losing soundness. We present techniques for learning clauses during a branch and bound (B&B) MAXSAT search, a process that is more complicated than standard clause learning. To exploit these learnt clauses we develop a connection between them and bounds that can be used during B&B. This connection involves formulating a hitting set problem and finding bounds on its optimal solution. We present some new techniques for generating useful hitting set bounds and also show how linear and integer programs can be exploited for this purpose, opening the door for a hybrid approach to solving MAXSAT.