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

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Algorithms and Computation (ISAAC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3341))

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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.

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Author information

Authors and Affiliations

  1. Institute of Advanced Computer Studies, University of Maryland, College Park, MD, 20742, USA

    Joseph JaJa & Qingmin Shi

  2. IT University of Copenhagen, Rued Langgaardsvej 7, 2300, København S, Denmark

    Christian W. Mortensen

Authors
  1. Joseph JaJa
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  2. Christian W. Mortensen
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  3. Qingmin Shi
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Fudan University, 200433, Shanghai, China

    Rudolf Fleischer

  2. Department of Computer Science, The Hong Kong University of Science and Technology, Hong Kong

    Gerhard Trippen

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© 2004 Springer-Verlag Berlin Heidelberg

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JaJa, J., Mortensen, C.W., Shi, Q. (2004). Space-Efficient and Fast Algorithms for Multidimensional Dominance Reporting and Counting. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_49

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  • DOI: https://doi.org/10.1007/978-3-540-30551-4_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24131-7

  • Online ISBN: 978-3-540-30551-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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