Optimal Planar Orthogonal Skyline Counting Queries

  • Gerth Stølting Brodal
  • Kasper Green Larsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)

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 \(\Omega(\lg n/\lg\lg n)\).

Keywords

Query Time Space Usage Skyline Query Rightmost Point Orthogonal Range 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Kasper Green Larsen
    • 1
  1. 1.MADALGO, Department of Computer ScienceAarhus UniversityDenmark

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