An Ω lower bound for computing the sum of even-ranked elements

Mörig, Marc; Rautenbach, Dieter; Smid, Michiel; Tusch, Jan

Given a sequence A of 2n real numbers, the \ers\ problem asks for the sum of the n values that are at the even positions in the sorted order of the elements in A. We prove that, in the algebraic computation-tree model, this problem has time complexity \Theta(n \log n). This solves an open problem posed by Michael Shamos at the Canadian Conference on Computational Geometry in 2008.


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