Given a query object q, reverse k-nearest neighbor (RkNN) search aims to locate those objects of the database that have q among their k-nearest neighbors. In this paper, we propose an approximation method for solving RkNN queries, where the pruning operations and termination tests are guided by a characterization of the intrinsic dimensionality of the data. The method can accommodate any index structure supporting incremental (forward) nearest-neighbor search for the generation and verification of candidates, while avoiding impractically-high preprocessing costs. We also provide experimental evidence that our method significantly outperforms its competitors in terms of the tradeoff between execution time and the quality of the approximation. Our approach thus addresses many of the scalability issues surrounding the use of previous methods in data mining.