MGR: Efficiently Processing Maximal Group Reverse k Nearest Neighbors Queries

Abstract

Given a set of facilities and a set of clients, a reverse <i>k</i> nearest neighbors (R<i>k</i>NN) query returns every client for which the query facility is one of the <i>k</i>-closest facilities. R<i>k</i>NN query has been studied thoroughly for its importance in various fields such as facility location. In this paper, we propose a brand new variant of R<i>k</i>NN query, namely, maximal group reverse <i>k</i> nearest neighbors (MaxGroupR<i>k</i>NN) query. Given a set of clients, a set of candidate facilities and parameters <i>k</i> and <i>m</i>, MaxGroupRkNN query returns a set of <i>m</i> facilities out of the candidates, such that the total number of R<i>k</i>NNs of the result set is maximized. The MaxGroupR<i>k</i>NN query is important for multi-facility location problem, which aims to maximize the total potential clients of a group of facility providing the same service such as chain stores, charging stations and logistic centers. A straightforward solution is to enumerate all possible combinations which is obviously time consuming. In order to address this problem, we present an efficient solution namely MGR, which is based on a well designed pruning technique. The proposed pruning technique is able to filter out the candidates that cannot contribute to the final result and reduce the computation cost dramatically. Moreover, we propose a well-designed optimization technique that can further reduce the computation cost. A detailed theoretical analysis of our methods is provided and the experimental results also confirm that our proposed methods have high efficiency and scalability.