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Space-Efficient and Fast Algorithms for Multidimensional Dominance Reporting and Counting

  • Joseph JaJa
  • Christian W. Mortensen
  • Qingmin Shi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3341)

Abstract

We present linear-space sub-logarithmic algorithms for handling the 3-dimensional dominance reporting and the 2-dimensional dominance counting problems. Under the RAM model as described in [M. L. Fredman and D. E. Willard. “Surpassing the information theoretic bound with fusion trees”, Journal of Computer and System Sciences, 47:424–436, 1993], our algorithms achieve O(log n/loglog n+f) query time for the 3-dimensional dominance reporting problem, where f is the output size, and O(log n/loglog n) query time for the 2-dimensional dominance counting problem. We extend these results to any constant dimension d ≥ 3, achieving O(n(log n/loglog n) d − 3) space and O((log n/loglog n) d − 2+ f) query time for the reporting case and O(n(log n/loglog n) d − 2) space and O((log n/loglog n) d − 1) query time for the counting case.

Keywords

Internal Node Query Point Query Time Space Usage Dimensional Point 
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-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Joseph JaJa
    • 1
  • Christian W. Mortensen
    • 2
  • Qingmin Shi
    • 1
  1. 1.Institute of Advanced Computer StudiesUniversity of MarylandCollege ParkUSA
  2. 2.IT University of CopenhagenKøbenhavn SDenmark

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