Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Detecting IIS in infeasible linear programmes using techniques from goal programming
Computers and Operations Research
Consistency restoriation and explanations in dynamic CSPs----application to configuration
Artificial Intelligence
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Boosting complete techniques thanks to local search methods
Annals of Mathematics and Artificial Intelligence
Analyzing Infeasible Mixed-Integer and Integer Linear Programs
INFORMS Journal on Computing
Fast Heuristics for the Maximum Feasible Subsystem Problem
INFORMS Journal on Computing
Finding the chromatic number by means of critical graphs
Journal of Experimental Algorithmics (JEA)
Efficient algorithms for finding critical subgraphs
Discrete Applied Mathematics
Efficient algorithms for finding critical subgraphs
Discrete Applied Mathematics
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Survey: Covering problems in facility location: A review
Computers and Industrial Engineering
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Given a finite set E and a family F={E"1,...,E"m} of subsets of E such that F covers E, the famous unicost set covering problem (USCP) is to determine the smallest possible subset of F that also covers E. We study in this paper a variant, called the Large Set Covering Problem (LSCP), which differs from the USCP in that E and the subsets E"i are not given in extension because they are very large sets that are possibly infinite. We propose three exact algorithms for solving the LSCP. Two of them determine minimal covers, while the third one produces minimum covers. Heuristic versions of these algorithms are also proposed and analysed. We then give several procedures for the computation of a lower bound on the minimum size of a cover. We finally present algorithms for finding the largest possible subset of F that does not cover E. We also show that a particular case of the LSCP is to determine irreducible infeasible sets in inconsistent constraint satisfaction problems. All concepts presented in the paper are illustrated on the k-colouring problem which is formulated as a constraint satisfaction problem.