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A General Framework for MaxRS and MaxCRS Monitoring in Spatial Data Streams

This article addresses the MaxRS (Maximizing Range Sum) monitoring problem. Given a set of weighted spatial stream objects, this problem is to monitor a location of a user-specified sized rectangle where the sum of the weights of the objects covered by the rectangle is maximized. This problem supports modern applications (e.g., traffic analysis and event detection in urban sensing) but has not yet been addressed. Although some algorithms for static objects have been proposed, such algorithms are not scalable to stream environments. These motivate us to devise an algorithm for efficient MaxRS monitoring. We first propose G2 (Graph in Grid index) and a G2-based algorithm to incrementally update the result. We then propose aG2 (aggregate G2), by enhancing G2, and a branch-and-bound algorithm that employs aG2 and can deal with error-guaranteed approximation. We also address MaxCRS monitoring, which is the circle version of the aforementioned problem. Its importance is evident from the fact that distance is also popular as a range criterion. We then have an emerging challenge of developing a general and efficient solution for both continuous MaxRS and MaxCRS queries. Based on a common property of the two problems, we generalize aG2 so as to be employed in both continuous MaxRS and MaxCRS queries. The branch-and-bound algorithm is also extended to suit the generalized index. We conduct extensive experiments using synthetic and real datasets. The experimental results show that our algorithms support a fast result update and significantly outperform the algorithms for static data.