### Efficient Reverse k-Nearest Neighbor Estimation

*Elke Achtert*

*, Christian Böhm*

*, Peer Kröger*

*, Peter Kunath*

*, Alexey Pryakhin*

*and Matthias Renz*

#### Abstract

The reverse k-nearest neighbor (RkNN) problem, i.e. finding all objects in a data set the k-nearest neighbors of which include a specified query object, has received increasing attention recently. Many industrial and scientific applications call for solutions of the RkNN problem in arbitrary metric spaces where the data objects are not Euclidean and only a metric distance function is given for specifying object similarity. Usually, these applications need a solution for the generalized problem where the value of k is not known in advance and may change from query to query. In addition, many applications require a fast approximate answer of RkNN-queries. For these scenarios, it is important to generate a fast answer with high recall. In this paper, we propose the first approach for efficient approximative RkNN search in arbitrary metric spaces where the value of k is specified at query time. Our approach uses the advantages of existing metric index structures but proposes to use an approximation of the nearest-neighbor-distances in order to prune the search space. We show that our method scales significantly better than existing non-approximative approaches while producing an approximation of the true query result with a high recall.

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