A scalable algorithm for maximizing range sum in spatial databases

Abstract

This paper investigates the MaxRS problem in spatial databases. Given a set O of weighted points and a rectangular region r of a given size, the goal of the MaxRS problem is to find a location of r such that the sum of the weights of all the points covered by r is maximized. This problem is useful in many location-based applications such as finding the best place for a new franchise store with a limited delivery range and finding the most attractive place for a tourist with a limited reachable range. However, the problem has been studied mainly in theory, particularly, in computational geometry. The existing algorithms from the computational geometry community are in-memory algorithms which do not guarantee the scalability. In this paper, we propose a scalable external-memory algorithm (ExactMaxRS ) for the MaxRS problem, which is optimal in terms of the I/O complexity. Furthermore, we propose an approximation algorithm (ApproxMaxCRS ) for the MaxCRS problem that is a circle version of the MaxRS problem. We prove the correctness and optimality of the ExactMaxRS algorithm along with the approximation bound of the ApproxMaxCRS algorithm. From extensive experimental results, we show that the ExactMaxRS algorithm is two orders of magnitude faster than methods adapted from existing algorithms, and the approximation bound in practice is much better than the theoretical bound of the ApproxMaxCRS algorithm.

Efficient Evaluation of Maximizing Range Sum Queries in a Road Network

“…We first remind the idea of transforming the max-enclosing rectangle query into the rectangle intersection query [4], which is the fundamental idea for processing MaxRS queries in Euclidean space [1].…”

“…The edge-record processing algorithm is denoted by ProcessEdge in the EA method (Algorithm 3). First, ProcessEdge checks if the edge-record of current processed edge is in the in-memory HRT (lines [1][2][3][4][5]. If the edgerecord is in the in-memory HRT, ProcessEdge scans the edge-record to find the max-segments, and ProcessEdge removes the edge-record from the in-memory HRT (lines 6-7).…”

“…Those methods are internal memory algorithms. Choi et al [1] proposed an algorithm for solving MaxRS problem in the case of external memory with optimal I/O's. Choi et al [16] also extended the MaxRS problem to be more fundamental, namely AllMaxRS, so that all the locations with the same best score can be retrieved.…”

“…Most traditional studies on spatial databases have focused on finding nearby data objects (e.g., range queries and nearest neighbor queries), rather than finding the best location to optimize a certain objective. Recently, a maximizing range sum (MaxRS) query was introduced [1]. Given a set of positive-weighted points and a query rectangle r of a given size, the goal of a MaxRS query is to find the optimal location of r such that the sum of the weights of all the points covered by r is maximized.…”

“…To process MaxRS queries on Euclidean space, Choi et al [1] proposed an external-memory algorithm, while Imai and Asano [2] proposed an in-memory algorithm. In many real-life location-based services, however, the motion of a client may be constrained by an underlying (spatial) road network.…”