Median Selection Requires $(2+\epsilon)n$ Comparisons

Source abstract

Improving a long standing result of Bent and John [Proceedings of the 17th Annual ACM Symposium on Theory of Computing, Providence, RI, 1985, pp. 213--216], and extending a recent result of Dor, Håstad, Ulfberg, and Zwick [ SIAM J. Discrete Math., 14 (2001), pp. 299--311], we obtain a $(2{+}\epsilon)n$ lower bound (for some fixed $\epsilon>0$) on the number of comparisons required, in the worst case, for selecting the median of n elements.