On selecting thek largest with median tests

Abstract

LetW itk(n) be the minimax complexity of selecting thek largest elements ofn numbersx 1,x 2,...,x n by pairwise comparisonsx i :x j . It is well known thatW 2(n) =n−2+ [lgn], andW k (n) = n + (k−1)lg n +O(1) for all fixed k ≥ 3. In this paper we studyW k (n), the minimax complexity of selecting thek largest, when tests of the form “Isx i the median of {x i ,x j ,x t }?” are also allowed. It is proved thatW2(n) =n−2+ [lgn], andW k (n) =n + (k−1)lg2 n +O(1) for all fixedk≥3.

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This research was supported in part by the National Science Foundation under Grant No. DCR-8308109.

Communicated by C. K. Wong.

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Chi-Chih Yao, A. On selecting thek largest with median tests. Algorithmica 4, 293–300 (1989). https://doi.org/10.1007/BF01553891

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Key words

  • Algorithm
  • Complexity
  • Decision tree
  • Median test
  • Selection