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On computing majority by comparisons

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Abstract

The elements of a finite setX (of odd cardinalityn) are divided into two (as yet unknown) classes and a member of the larger class is to be identified. The basic operation is to test whether two objects are in the same class. We show thatn-B(n) comparisons are necessary and sufficient in worst case, whereB(n) is the number of 1's in the binary expansion ofn.

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Author information

Author notes

  1. Michael Werman

    Present address: Department of Computer Science, Hebrew University, Givat Ram Jerusalem, Israel

  2. Michael E. Saks

    Present address: Department of Computer Science and Engineering, Mail Code 0114, University of California, San Diego, 92093-0114, La Jolla, CA, USA

Authors and Affiliations

  1. Department of Mathematics and RUTCOR, Rutgers University, 08903, New Brunswick, NJ

    Michael E. Saks

  2. Institute for Mathematics and its Applications, University of Minnesota, 55455, Minneapolis, Minn, USA

    Michael Werman

  3. Bell Communications Research, 07960, Morristown, NJ, USA

    Michael E. Saks

Authors
  1. Michael E. Saks
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  2. Michael Werman
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Additional information

Supported in part by NSF grant DMS87 03541 and Air Force Office of Scientific Research grant AFOSR-0271.

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Saks, M.E., Werman, M. On computing majority by comparisons. Combinatorica 11, 383–387 (1991). https://doi.org/10.1007/BF01275672

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  • DOI: https://doi.org/10.1007/BF01275672

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