SLICE: Reviving regions-based pruning for reverse k nearest neighbors queries

Given a set of facilities and a set of users, a reverse k nearest neighbors (RkNN) query q returns every user for which the query facility is one of the k-closest facilities. Due to its importance, RkNN query has received significant research attention in the past few years. Almost all of the existing techniques adopt a pruning-and-verification framework. Regions-based pruning and half-space pruning are the two most notable pruning strategies. The half-space based approach prunes a larger area and is generally believed to be superior. Influenced by this perception, almost all existing RkNN algorithms utilize and improve the half-space pruning strategy. We observe the weaknesses and strengths of both strategies and discover that the regions-based pruning has certain strengths that have not been exploited in the past. Motivated by this, we present a new RkNN algorithm called SLICE that utilizes the strength of regions-based pruning and overcomes its limitations. Our extensive experimental study on synthetic and real data sets demonstrate that SLICE is significantly more efficient than the existing algorithms. We also provide a detailed theoretical analysis to analyze various aspects of our algorithm such as I/O cost, the unpruned area, and the cost of its verification phase etc. The experimental study validates our theoretical analysis.