On lower bounds for selectinc the median

We present a reformulation of the 2n + o(n) lower bound of Bent and John [Proceedings of the 17th Annual ACM Symposium on Theory of Computing, 1985, pp. 213-216] for the number of comparisons needed for selecting the median of n elements. Our reformulation uses a weight function. Apart from giving a more intuitive proof for the lower bound, the new formulation opens up possibilities for improving it. We use the new formulation to show that any pair-forming median finding algorithm, i.e., a median finding algorithm that starts by comparing [n/2] disjoint pairs of elements must perform, in the worst case, at least 2.01n + o(n) comparisons. This provides strong evidence that selecting the median requires at least cn + o(n) comparisons for some c > 2.