On Exact Selection of Minimally Unsatisfiable Subformulae
Annals of Mathematics and Artificial Intelligence
Solution techniques for the Large Set Covering Problem
Discrete Applied Mathematics
Generalized filtering algorithms for infeasibility analysis
Computers and Operations Research
Computers and Operations Research
On the approximability of the maximum feasible subsystem problem with 0/1-coefficients
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On optimal zero-preserving corrections for inconsistent linear systems
Journal of Global Optimization
Using Satisfiability Modulo Theories for Inductive Verification of Lustre Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Minimal infeasible constraint sets in convex integer programs
Journal of Global Optimization
Lemma learning in SMT on linear constraints
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Concurrent architecture and schedule optimization of time-triggered automotive systems
Proceedings of the eighth IEEE/ACM/IFIP international conference on Hardware/software codesign and system synthesis
Priority assignment for event-triggered systems using mathematical programming
Proceedings of the Conference on Design, Automation and Test in Europe
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Algorithms and computer-based tools for analyzing infeasible linear and nonlinear programs have been developed in recent years, but few such tools exist for infeasible mixed-integer or integer linear programs. One approach that has proven especially useful for infeasible linear programs is the isolation of an Irreducible Infeasible Set of constraints (IIS), a subset of the constraints defining the overall linear program that is itself infeasible, but for which any proper subset is feasible. Isolating an IIS from the larger model speeds the diagnosis and repair of the model by focussing the analytic effort. This paper describes and tests algorithms for finding small infeasible sets in infeasible mixed-integer and integer linear programs; where possible these small sets are IISs.