English

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

Data Structures and Algorithms 2009-03-23 v2

Abstract

Given a sequence A of 2n real numbers, the Even-Rank-Sum 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.

Cite

@article{arxiv.0901.0930,
  title  = {An \Omega(n log n) lower bound for computing the sum of even-ranked elements},
  author = {Marc Mörig and Dieter Rautenbach and Michiel Smid and Jan Tusch},
  journal= {arXiv preprint arXiv:0901.0930},
  year   = {2009}
}
R2 v1 2026-06-21T11:58:29.435Z