Visible reverse k-Nearest neighbor queries

Reverse nearest neighbor (RNN) queries have a broad application base such as decision support, profile-based marketing, resource allocation, data mining, etc. Previous work on RNN search does not take obstacles into consideration. In the real world, however, there are many physical obstacles (e.g., buildings, blindages, etc.), and their presence may affect the visibility/distance between two objects. In this paper, we introduce a novel variant of RNN queries, namely visible reverse nearest neighbor (VRNN) search, which considers the obstacle influence on the visibility of objects. Given a data set P, an obstacle set O, and a query point q, a VRNN query retrieves the points in P that have q as their nearest neighbor and are visible to q. We propose an efficient algorithm for VRNN query processing, assuming that both P and O are indexed by R-trees. Our method does not require any pre-processing, and employs half-plane property and visibility check to prune the search space.