An Omega(n log n) lower bound for computing the sum of even-ranked elements
Given a sequence A of 2n real numbers, the EvenRankSum problem asks for the SLIM of the It 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. (C) 2009 Elsevier B.V. All rights reserved.
lower bounds order statistics computational complexity