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In this paper we show that the minimum number of comparisons necessary for the computation of the kth element of a totally ordered set of size n, Vₖ (n), is bounded below by n - k + (k - 1) log ₂ (n/(k - 1)). For $3 < k < n/4$, this bound is an improvement on the best lower bound presently known. A new algorithm which yields an upper bound that is better than the currently known bound for a large range of values of n will also be presented.
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Laurent Hyafil (1976) studied this question.
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