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Existing models for nearest neighbor search in multidimensional spaces are not appropriate for query optimization because they either lead to erroneous estimation or involve complex equations that are expensive to evaluate in real-time. This article proposes an alternative method that captures the performance of nearest neighbor queries using approximation. For uniform data, our model involves closed formulae that are very efficient to compute and accurate for up to 10 dimensions. Further, the proposed equations can be applied on nonuniform data with the aid of histograms. We demonstrate the effectiveness of the model by using it to solve several optimization problems related to nearest neighbor search.