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

@article{Plvlgyi2011LowerBF,
  title={Lower bounds for finding the maximum and minimum elements with k lies},
  author={D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi},
  journal={CoRR},
  year={2011},
  volume={abs/1111.3288}
}
In this paper we deal with the problem of nding 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 xed constant. We prove that at least (k+1.5)n+Θ(k) comparisons are needed in the worst case thus disproving the conjecture that (k+1+ )n comparisons are enough. 

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