Selecting the k largest elements with parity tests

Abstract

In this paper we study the problem of finding the k largest elements of n distinct real numbers. We give a pure combinatorial argument to prove that n + (k - 1) log n + O(1) queries are necessary for any deterministic algorithm using parity tests only. This settles an open problem first raised by Yao [11]. We also present a randomized algorithm with error probability O(1/nc) using only O(log2 n+k log n) parity tests, where c > 1 is any fixed constant. © Springer-Verlag Berlin Heidelberg 1998.