The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
On approximation algorithms for the minimum satisfiability problem
Information Processing Letters
Towards a universal test suite for combinatorial auction algorithms
Proceedings of the 2nd ACM conference on Electronic commerce
Approximating MIN 2-SAT and MIN 3-SAT
Theory of Computing Systems
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
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Taming the computational complexity of combinatorial auctions: optimal and approximate approaches
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Soft arc consistency revisited
Artificial Intelligence
Resolution-based lower bounds in MaxSAT
Constraints
Combining Graph Structure Exploitation and Propositional Reasoning for the Maximum Clique Problem
ICTAI '10 Proceedings of the 2010 22nd IEEE International Conference on Tools with Artificial Intelligence - Volume 01
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Optimizing with minimum satisfiability
Artificial Intelligence
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
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We define solving techniques for the Minimum Satisfiability Problem (MinSAT), propose an efficient branch-and-bound algorithm to solve the Weighted Partial MinSAT problem, and report on an empirical evaluation of the algorithm on Min-3SAT, Max-Clique, and combinatorial auction problems. Techniques solving MinSAT are substantially different from those for the Maximum Satisfiability Problem (MaxSAT). Our results provide empirical evidence that solving combinatorial optimization problems by reducing them to MinSAT may be substantially faster than reducing them to MaxSAT, and even competitive with specific algorithms. We also use MinSAT to study an interesting correlation between the minimum number and the maximum number of satisfied clauses of a SAT instance.