Top-k Manhattan Spatial Skyline Queries
Efficiently retrieving relevant data from a huge spatial database is and has been the subject of research in fields like database systems, geographic information systems and also computational geometry for many years. In this context, we study the retrieval of relevant points with respect to a query and a scoring function: let P and Q be point sets in the plane, the skyline of P with respect to Q consists of points P for which no other point of P is closer to all points of Q. A skyline of a point set P with respect to a query set Q can be seen as the most “relevant” or “desirable” subset of P with respect to Q. As the skyline of a set P can be as large as the set P itself, it is reasonable to filter the skyline using a scoring function f, only reporting the k best skyline points with respect to f.
In this paper, we consider the top-k Manhattan spatial skyline query problem for monotone scoring functions, where distances are measured in the L1 metric. We present an algorithm that computes the top-k skyline points in near linear time in the size of P. The presented strategy improves over the direct approach of first using the state-of-the-art algorithm to compute the Manhattan spatial skyline  and then filtering it by the scoring function by a log(|P|) factor. The improvement has been validated in experiments that show a speedup of up to an order of magnitude.
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