Range Aggregate Maximal Points in the Plane

  • Ananda Swarup Das
  • Prosenjit Gupta
  • Anil Kishore Kalavagattu
  • Jatin Agarwal
  • Kannan Srinathan
  • Kishore Kothapalli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7157)

Abstract

In this work, we study the problem of reporting and counting maximal points in a query rectangle for a set of n integer points that lie on an n×n grid. A point is said to be maximal inside a query rectangle if it is not dominated by any other point inside the query rectangle. Our model of computation is unit-cost RAM model with word size of O(logn) bits. For the reporting version of the problem, we present a data structure of size \(O(n\frac{\log n}{\log\log n})\) words and support querying in \(O(\frac{\log n}{\log\log n}+k)\) time where k is the size of the output. For the counting version, we present a data structure of size \(O(n\frac{\log^{2} n}{\log\log n})\) words which supports querying in \(O(\frac{\log^{\frac{3}{2}}n} {\log\log n})\). Both the data structures are static in nature. The reporting version of the problem has been studied in [1] and [5]. To the best of our knowledge, this is the first sub-logarithmic result for the reporting version and the first work for the counting version of the problem.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ananda Swarup Das
    • 1
  • Prosenjit Gupta
    • 2
  • Anil Kishore Kalavagattu
    • 3
  • Jatin Agarwal
    • 3
  • Kannan Srinathan
    • 3
  • Kishore Kothapalli
    • 3
  1. 1.Kalinga Institute of Industrial TechnologyBhubaneswarIndia
  2. 2.Heritage Institute of TechnologyKolkataIndia
  3. 3.International Institute of Information TechnologyHyderabadIndia

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