On selecting thek largest with median tests |
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Authors: | Andrew Chi-Chih Yao |
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Affiliation: | 1. Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA
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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 thatW′2(n) =n?2+ lgn], andW′ k (n) =n + (k?1)lg2 n +O(1) for all fixedk≥3. |
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