Reverse k-nearest neighbor search in the presence of obstacles

In this paper, we study a new form of reverse nearest neighbor (RNN) queries, i.e., obstructed reverse nearest neighbor (ORNN) search. It considers the impact of obstacles on the distance between objects, which is ignored by the existing work on RNN retrieval. Given a data set P, an obstacle set O, and a query point q in a two-dimensional space, an ORNN query finds from P, all the points/objects that have q as their nearest neighbor, according to the obstructed distance metric, i.e., the length of the shortest path between two points without crossing any obstacle. We formalize ORNN search, develop effective pruning heuristics (via introducing a novel concept of boundary region), and propose efficient algorithms for ORNN query processing assuming that both P and O are indexed by traditional data-partitioning indexes (e.g., R-trees). In addition, several interesting variations of ORNN queries, namely, obstructed reverse k-nearest neighbor (ORkNN) search, ORkNN search with maximum obstructed distance δ (δ-ORkNN), and constrained ORkNN (CORkNN) search, have been introduced, and they can be tackled by extending the ORNN query techniques, which demonstrates the flexibility of the proposed ORNN query algorithm. Extensive experimental evaluation using both real and synthetic data sets verifies the effectiveness of pruning heuristics and the performance of algorithms, respectively.