Continuous evaluation of monochromatic and bichromatic 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 as it is applicable for both the monochromatic and bichromatic reverse nearest neighbor queries. The incremental aspect of IGERN is achieved through determining only a small set of objects to be monitored. While previous algorithms for monochromatic queries rely mainly on monitoring six pie regions, IGERN takes a radical approach by monitoring only a single region around the query object. The IGERN algorithm clearly outperforms the state-of-theart algorithms in monochromatic queries. In addition, the IGERN algorithm presents the first attempt for continuous evaluation of bichromatic reverse nearest neighbor queries. The computational complexity of IGERN is presented in comparison to the state-of-the-art algorithms in the monochromatic case and to the use of Voronoi diagrams for the bichromatic case. In addition, the correctness of IGERN in both the monochromatic and bichromatic cases are proved. Extensive experimental analysis shows that IGERN is efficient, is scalable, and outperforms previous techniques for continuous reverse nearest neighbor queries.