A new approach for maximizing bichromatic reverse nearest neighbor search

Maximizing bichromatic reverse nearest neighbor (MaxBRNN) is a variant of bichromatic reverse nearest neighbor (BRNN). The purpose of the MaxBRNN problem is to find an optimal region that maximizes the size of BRNNs. This problem has lots of real applications such as location planning and profile-based marketing. The best-known algorithm for the MaxBRNN problem is called MaxOverlap. In this paper, we study the MaxBRNN problem and propose a new approach called MaxSegment for a two-dimensional space when the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}-norm is used. Then, we extend our algorithm to other variations of the MaxBRNN problem such as the MaxBRNN problem with other metric spaces, and a three-dimensional space. Finally, we conducted experiments on real and synthetic datasets to compare our proposed algorithm with existing algorithms. The experimental results verify the efficiency of our proposed approach.