Incremental and general evaluation of reverse nearest neighbors

This paper presents a novel algorithm for Incremental and General Evaluation of continuous Reverse Nearest neighbor queries (IGERN, for short). The IGERN algorithm is general in that it is applicable for both continuous monochromatic and bichromatic reverse nearest neighbor queries. This problem is faced in a number of applications such as enhanced 911 services and in army strategic planning. A main challenge in these problems is to maintain the most up-to-date query answers as the data set frequently changes over time. Previous algorithms for monochromatic continuous reverse nearest neighbor queries rely mainly on monitoring at the worst case of six pie regions, whereas IGERN takes a radical approach by monitoring only a single region around the query object. The IGERN algorithm clearly outperforms the state-of-the-art algorithms in monochromatic queries. We also propose a new optimization for the monochromatic IGERN to reduce the number of nearest neighbor searches. Furthermore, a filter and refine approach for IGERN (FR-IGERN) is proposed for the continuous evaluation of bichromatic reverse nearest neighbor queries which is an optimized version of our previous approach. The computational complexity of IGERN and FR-IGERN is presented in comparison to the state-of-the-art algorithms in the monochromatic and bichromatic cases. In addition, the correctness of IGERN and FR-IGERN in both the monochromatic and bichromatic cases, respectively, are proved. Extensive experimental analysis using synthetic and real data sets shows that IGERN and FR-IGERN is efficient, is scalable, and outperforms previous techniques for continuous reverse nearest neighbor queries.