Improved randomized selection

We show that several versions of Floyd and Rivest’s improved algorithm Select for finding the kth smallest of n elements require at most n + min{k, n − k} + O(n 1/2 ln 1/2 n) comparisons on average and with high probability. This rectifies the analysis of Floyd and Rivest, and extends it to the case of nondistinct elements. Encouraging computational results on large median-finding problems are reported.

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