Selecting the k largest elements with parity tests Original Research Article

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. 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.