Some results and experiments in programming techniques for propositional logic
Computers and Operations Research - Special issue: Applications of integer programming
Mathematical Programming: Series A and B
Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Improvements to propositional satisfiability search algorithms
Improvements to propositional satisfiability search algorithms
Linear programming 1: introduction
Linear programming 1: introduction
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
New upper bounds for maximum satisfiability
Journal of Algorithms
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Random MAX SAT, random MAX CUT, and their phase transitions
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Enhancing Maximum Satisfiablility Algorithms with Pure Literal Strategies
AI '96 Proceedings of the 11th Biennial Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Generic ILP versus specialized 0-1 ILP: an update
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Inference methods for a pseudo-boolean satisfiability solver
Eighteenth national conference on Artificial intelligence
Using weighted MAX-SAT engines to solve MPE
Eighteenth national conference on Artificial intelligence
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Study of lower bound functions for MAX-2-SAT
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Evidence for invariants in local search
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Exact Max-SAT solvers for over-constrained problems
Journal of Heuristics
Quartet-Based Phylogeny Reconstruction with Answer Set Programming
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Artificial Intelligence
Comparing action descriptions based on semantic preferences
Annals of Mathematics and Artificial Intelligence
A logical approach to efficient Max-SAT solving
Artificial Intelligence
SOFIE: a self-organizing framework for information extraction
Proceedings of the 18th international conference on World wide web
Solving Optimization Problems with DLL
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
A new Approach for Solving Satisfiability Problems with Qualitative Preferences
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
New inference rules for efficient Max-SAT solving
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Detecting disjoint inconsistent subformulas for computing lower bounds for Max-SAT
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Within-problem learning for efficient lower bound computation in Max-SAT solving
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
New inference rules for Max-SAT
Journal of Artificial Intelligence Research
MINIMAXSAT: an efficient weighted max-SAT solver
Journal of Artificial Intelligence Research
Exploiting inference rules to compute lower bounds for MAX-SAT solving
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Solving satisfiability problems with preferences
Constraints
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Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the Davis-Putnam-Logemann-Loveland procedure (DPLL) is one of the most competitive exact algorithms for solving max-SAT. In this paper, we propose and investigate a number of strategies for max-SAT. The first strategy is a set of unit propagation or unit resolution rules for max-SAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of max-SAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a binary-clause first rule and a dynamic-weighting variable ordering rule, which are motivated by a thorough analysis of two existing well-known variable orderings. Based on the analysis of these strategies, we develop an exact solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from the max-SAT libraries show that our new solver outperforms most of the existing exact max-SAT solvers, with orders of magnitude of improvement in many cases.