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Given a sequence A of 2n real numbers, the Even-Rank-Sum problem asks for thesum of the n values that are at the even positions in the sorted order of theelements in A. We prove that, in the algebraic computation-tree model, thisproblem has time complexity \Theta(n log n). This solves an open problem posedby Michael Shamos at the Canadian Conference on Computational Geometry in 2008.

An \Omega(n log n) lower bound for computing the sum of even-ranked elements