On computing majority by comparisons

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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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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AMS subject classification (1991)

  • 68 P 10
  • 68 R 05