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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bollobás, B., Extremal Graph Theory. Academic Press, 1978.
Campbell, D. and McNeill, T., Finding a majority when sorting is not available. The Computer Journal 34 (1991) 186.
Fischer, M. J. and Salzburg S. L., Solution to problem 81-5. Journal of Algorithms 3 (1982) 376–379.
Matula, D. W., An Optimal Algorithm for the Majority Problem. Manuscript, Southern Methodist University, Texas, 1990.
Misra, J. and Gries, D., Finding Repeated Elements. Science of Computer Programming 2 (1982) 143–152.
Moore, J., Problem 81-5. Journal of Algorithms 2 (1981) 208–209.
Saks, M. E. and Werman, M., On Computing Majority by Comparisons. Combinatorica 11 (1991) 383–387.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-57182-5_38
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57182-7
Online ISBN: 978-3-540-47927-7
eBook Packages: Springer Book Archive