| Summary: | In this paper, we introduce the three-dimensional Maximum Range-Sum (3D MaxRS) problem and the Maximum Spatiotemporal Range-Sum Change (MaxStRSC) problem. The 3D MaxRS problem tries to find the 3D range where the sum of weights across all objects inside is maximized, and the MaxStRSC problem tries to find the spatiotemporal range where the sum of weights across all objects inside is maximally increased. The goal of this paper is to provide efficient methods for data analysts to find interesting spatiotemporal regions in a large historical spatiotemporal dataset by addressing two problems. We provide a mathematical explanation for each problem and propose several algorithms for them. Existing methods tried to find the optimal region over two-dimensional datasets or to monitor a burst region over two-dimensional data streams. The majority of them cannot directly solve our problems. Although some existing methods can be used or modified to solve the 3D MaxRS problems, they have limited scalability. In addition, none of them can be used to solve the MaxStRS-RC problem (a type of MaxStRSC problem). Finally, we study the performance of the proposed algorithms experimentally. The experimental results show that the proposed algorithms are scalable and much more efficient than existing methods.
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