Lower bounds for finding the maximum and minimum elements with k lies

Abstract

In this paper we deal with the problem of finding the smallest and the largest elements of a totally ordered set of size $n$ using pairwise comparisons if $k$ of the comparisons might be erroneous where $k$ is a fixed constant. We prove that at least $(k+1.5)n+\Theta (k)$ comparisons are needed in the worst case thus disproving the conjecture that $(k+1+\epsilon )n$ comparisons are enough.