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The complexity of finding replicas using equality tests

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Book cover Mathematical Foundations of Computer Science 1993 (MFCS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 711))

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Abstract

We prove (for fixed k) that at least \(\tfrac{1}{{k - 1}}(\begin{array}{*{20}c}n \\2 \\\end{array} ) - O(n)\) equality tests and no more than \(\tfrac{2}{k}(\begin{array}{*{20}c}n \\2 \\\end{array} ) + O(n)\) equality tests are needed in the worst case to determine whether a given set of n elements contains a subset of k identical elements. The upper bound is an improvement by a factor 2 compared to known results. We give tighter bounds for k=3.

This research was supported by the ESPRIT II BRA Programme of the EC under contract # 7141 (ALCOM II) and by CCI-Europe.

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Author information

Authors and Affiliations

  1. Computer Science Department, Aarhus University, 8000, Aarhus C, Denmark

    Gudmund Skovbjerg Frandsen, Peter Bro Miltersen & Sven Skyum

Authors
  1. Gudmund Skovbjerg Frandsen
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  2. Peter Bro Miltersen
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  3. Sven Skyum
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Editor information

Andrzej M. Borzyszkowski Stefan Sokołowski

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© 1993 Springer-Verlag Berlin Heidelberg

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Frandsen, G.S., Miltersen, P.B., Skyum, S. (1993). The complexity of finding replicas using equality tests. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_38

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  • DOI: https://doi.org/10.1007/3-540-57182-5_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57182-7

  • Online ISBN: 978-3-540-47927-7

  • eBook Packages: Springer Book Archive

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