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)


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.


Internal Node Query Point Query Time Space Usage Dimensional Point 
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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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