An Ω(n logn) lower bound for computing the sum of even-raked elements

Authors:
Marc Mörig;Dieter Rautenbach;Michiel Smid;Jan Tusch
Affiliations:
Faculty of Computer Science, University of Magdeburg, Magdeburg, Germany;Faculty of Mathematics and Natural Sciences, Ilmenau University of Technology, Ilmenau, Germany;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Faculty of Computer Science, University of Magdeburg, Magdeburg, Germany
Venue:
Information Processing Letters
Year:
2009

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STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing

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Abstract

Given a sequence A of 2n real numbers, the EvenRankSum 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 @Q(nlogn). This solves an open problem posed by Michael Shamos at the Canadian Conference on Computational Geometry in 2008.