The complexity of finding replicas using equality tests

  • Gudmund Skovbjerg Frandsen
  • Peter Bro Miltersen
  • Sven Skyum
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)


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.


Equivalence Class Correct Answer Identical Element Equality Test Equality Query 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Gudmund Skovbjerg Frandsen
    • 1
  • Peter Bro Miltersen
    • 1
  • Sven Skyum
    • 1
  1. 1.Computer Science DepartmentAarhus UniversityAarhus CDenmark

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