MGR: Efficiently Processing Maximal Group Reverse k Nearest Neighbors Queries

Given a set of facilities and a set of clients, a reverse
$k$
nearest neighbors (
$\text{R}k$
NN) query returns every client for which the query facility is one of the
$k$
-closest facilities.
$\text{R}k$
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
$\text{R}k$
NN query, namely, maximal group reverse
$k$
nearest neighbors (MaxGroupR
$k$
NN) query. Given a set of clients, a set of candidate facilities and parameters
$k$
and
$m$
, MaxGroupR
$k$
NN query returns a set of
$m$
facilities out of the candidates, such that the total number of
$\text{R}k$
NNs of the result set is maximized. The MaxGroupR
$k$
NN query is important for multi-facility location problem, which aims to maximize the total potential clients of a group of facilities 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.