A Data Warehouse (DW) is a data repository that integrates data from multiple sources and organizes the data according to a set of data structures called dimensions. Each dimension provides a perspective upon which the data can be viewed. In order to support an efficient processing of queries, a dimension is usually required to satisfy different classes of integrity constraints. In this paper, we study the problem of repairing a dimension when it fails to satisfy a set of two classes of integrity constraints: strictness constraints and covering constraints. We introduce the notion of minimal repair of a dimension in this context. A minimal repair is defined as a new dimension that is consistent with respect to the integrity constraints, which is obtained by applying a minimal amount of updates to the original dimension. We study the complexity of computing minimal repairs. Finally, we show how to characterize and compute minimal repairs of a dimension using Datalog programs with stable...