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Algorithmica

, Volume 4, Issue 1–4, pp 293–300 | Cite as

On selecting thek largest with median tests

  • Andrew Chi-Chih Yao
Article

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.

Key words

Algorithm Complexity Decision tree Median test Selection 

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Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • Andrew Chi-Chih Yao
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityPrincetonUSA

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