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arXiv 1208.0073cs.DB
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空间数据库中最大范围和的可扩展算法

A Scalable Algorithm for Maximizing Range Sum in Spatial Databases

Dong-Wan Choi, Chin-Wan Chung, Yufei Tao

摘要:

研究了空间数据库中的MaxRS问题。给定一组加权点O和一个给定大小的矩形区域r,MaxRS问题的目标是找到r的位置,使得r覆盖的所有点的权重之和最大化。这个问题在许多基于位置的应用中是有用的,例如为具有有限交付范围的新特许经营店找到最佳位置,以及为具有有限可达范围的游客找到最有吸引力的地方。然而,这个问题主要是在理论上,特别是在计算几何的研究。现有的计算几何算法都是内存算法,不能保证可扩展性。在本文中,我们提出了一个可扩展的外部存储器算法(ExactMaxRS)的MaxRS问题,这是最佳的I/O复杂度。此外,我们提出了一个近似算法(ApproxMaxCRS)的MaxCRS问题,是一个圆形版本的MaxRS问题。我们证明了ExactMaxRS算法的正确性和最优性以及ApproxMaxCRS算法的逼近界。从大量的实验结果,我们表明,ExactMaxRS算法是两个数量级的速度比现有的算法适应的方法,在实践中的近似界是远远优于理论界的ApproxMaxCRS算法。

英文摘要:

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.

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