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Bichromatic reverse nearest neighbor (BRNN) has been extensively studied in spatial database literature. In this paper, we study a related problem called MaxBRNN: find an optimal region that maximizes the size of BRNNs. Such a problem has many real life applications, including the problem of finding a new server point that attracts as many customers as possible by proximity. A straightforward approach is to determine the BRNNs for all possible points that are not feasible since there are a large (or infinite) number of possible points. To the best of our knowledge, the fastest known method has exponential time complexity on the data size. Based on some interesting properties of the problem, we come up with an efficient algorithm called MaxOverlap. Extensive experiments are conducted to show that our algorithm is many times faster than the best-known technique.

Trajectories of moving objects are collected in many applications. Raw trajectory data is typically very large, and has to be simplified before use. In this paper, we introduce the notion of directionpreserving trajectory simplification, and show both analytically and empirically that it can support a broader range of applications than traditional position-preserving trajectory simplification. We present a polynomial-time algorithm for optimal directionpreserving simplification, and another approximate algorithm with a quality guarantee. Extensive experimental evaluation with real trajectory data shows the benefit of the new techniques.