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This paper addresses how to answer the reversed nearest neighbor (RNN) queries in the location-based services when the privacy of users needs to be protected. We assume that the users' exact locations have been blurred into spatial regions based on user-specified privacy requirements. Inspired by the concept of Voronoi cell of point data, we introduce the concept of Voronoi cell for regions (VCR) and propose the framework to answer the privacy-ware RNN queries based on computing the VCR. We also propose the techniques to compute the VCR under L1 metric efficiently.