Space-Efficient and fast algorithms for multidimensional dominance reporting and counting

  • Authors:

  • Joseph JaJa;Christian W. Mortensen;Qingmin Shi

  • Affiliations:

  • Institute of Advanced Computer Studies, University of Maryland, College Park, MD;IT University of Copenhagen, København S, Denmark;Institute of Advanced Computer Studies, University of Maryland, College Park, MD

  • Venue:
  • ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
  • Year:
  • 2004

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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.