Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Arc-consistency and arc-consistency again
Artificial Intelligence
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
New upper bounds for maximum satisfiability
Journal of Algorithms
Towards a universal test suite for combinatorial auction algorithms
Proceedings of the 2nd ACM conference on Electronic commerce
A machine program for theorem-proving
Communications of the ACM
sub-SAT: a formulation for relaxed boolean satisfiability with applications in routing
Proceedings of the 2002 international symposium on Physical design
Computational Optimization and Applications
Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993
Nonserial Dynamic Programming
Resolution versus Search: Two Strategies for SAT
Journal of Automated Reasoning
An Algorithm for Optimal Winner Determination in Combinatorial Auctions
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Improved Exact Algorithms for MAX-SAT
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Node and arc consistency in weighted CSP
Eighteenth national conference on Artificial intelligence
Enhancing Davis Putnam with extended binary clause reasoning
Eighteenth national conference on Artificial intelligence
Using weighted MAX-SAT engines to solve MPE
Eighteenth national conference on Artificial intelligence
Constraint Processing
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Optimal Protein Structure Alignment Using Maximum Cliques
Operations Research
MaxSolver: an efficient exact algorithm for (weighted) maximum satisfiability
Artificial Intelligence
Study of lower bound functions for MAX-2-SAT
AAAI'04 Proceedings of the 19th national conference on Artifical 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
Journal of Artificial Intelligence Research
New inference rules for Max-SAT
Journal of Artificial Intelligence Research
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Existential arc consistency: getting closer to full arc consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
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
Neighborhood inverse consistency preprocessing
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Adding new clauses for faster local search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Improved exact solvers for weighted Max-SAT
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
On SAT modulo theories and optimization problems
SAT'06 Proceedings of the 9th 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
An algorithm for finding a maximum clique in a graph
Operations Research Letters
Preprocessing for controlled query evaluation with availability policy
Journal of Computer Security - 20th Annual IFIP WG 11.3 Working Conference on Data and Applications Security (DBSec'06)
Transforming Inconsistent Subformulas in MaxSAT Lower Bound Computation
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
A new Approach for Solving Satisfiability Problems with Qualitative Preferences
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Branch and Bound for Boolean Optimization and the Generation of Optimality Certificates
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
Algorithms for Weighted Boolean Optimization
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Max-ASP: Maximum Satisfiability of Answer Set Programs
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
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
Modelling Max-CSP as partial Max-SAT
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A Max-SAT inference-based pre-processing for Max-clique
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A declarative approach to robust weighted Max-SAT
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Resolution-based lower bounds in MaxSAT
Constraints
Balancing Optimality and Robustness in Resource Allocation Problems
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Using learnt clauses in MAXSAT
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A Framework for Certified Boolean Branch-and-Bound Optimization
Journal of Automated Reasoning
Journal of Automated Reasoning
Semiring-induced propositional logic: definition and basic algorithms
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
On the modelling and optimization of preferences in constraint-based temporal reasoning
Artificial Intelligence
Improving unsatisfiability-based algorithms for boolean optimization
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Using SAT-Solvers to compute inference-proof database instances
DPM'09/SETOP'09 Proceedings of the 4th international workshop, and Second international conference on Data Privacy Management and Autonomous Spontaneous Security
Read-once resolution for unsatisfiability-based Max-SAT algorithms
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Improvements to core-guided binary search for MaxSAT
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
A new encoding from MinSAT into MaxSAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Natural Max-SAT encoding of Min-SAT
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
Resolution procedures for multiple-valued optimization
Information Sciences: an International Journal
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Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques. Most of this work focuses on the computation of good quality lower bounds to be used within a branch and bound DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the logic that is behind. In this paper we introduce an original framework for Max-SAT that stresses the parallelism with classical SAT. Then, we extend the two basic SAT solving techniques: search and inference. We show that many algorithmic tricks used in state-of-the-art Max-SAT solvers are easily expressible in logical terms in a unified manner, using our framework. We also introduce an original search algorithm that performs a restricted amount of weighted resolution at each visited node. We empirically compare our algorithm with a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-SAT evaluation ever reported, demonstrate the practical usability of our approach.