Abstract
The skyline of a set of points in the plane is the subset of maximal points, where a point (x,y) is maximal if no other point (x′,y′) satisfies x′ ≥ x and y′ ≥ y. We consider the problem of preprocessing a set P of n points into a space efficient static data structure supporting orthogonal skyline counting queries, i.e. given a query rectangle R to report the size of the skyline of P ∩ R. We present a data structure for storing n points with integer coordinates having query time \(O(\lg n/\lg\lg n)\) and space usage O(n) words. The model of computation is a unit cost RAM with logarithmic word size. We prove that these bounds are the best possible by presenting a matching lower bound in the cell probe model with logarithmic word size: Space usage \(n\lg^{O(1)} n\) implies worst case query time \(\Omega(\lg n/\lg\lg n)\).
The full version of this paper is available at arxiv.org/abs/1304.7959
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Brodal, G.S., Larsen, K.G. (2014). Optimal Planar Orthogonal Skyline Counting Queries. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_10
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DOI: https://doi.org/10.1007/978-3-319-08404-6_10
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