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Constraint sets can become inconsistent in different contexts. For example, during a configuration session the set of customer requirements can become inconsistent with the configuration knowledge base. Another example is the engineering phase of a configuration knowledge base where the underlying constraints can become inconsistent with a set of test cases. In such situations we are in the need of techniques that support the identification of minimal sets of faulty constraints that have to be deleted in order to restore consistency. In this paper we introduce a divide and conquer-based diagnosis algorithm (FastDiag) that identifies minimal sets of faulty constraints in an overconstrained problem. This algorithm is specifically applicable in scenarios where the efficient identification of leading (preferred) diagnoses is crucial. We compare the performance of FastDiag with the conflict-directed calculation of hitting sets …