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 Θ (n log n). This solves an open problem posed by Michael Shamos at the Canadian Conference on Computational Geometry in 2008.

Additional Metadata
Keywords Computational complexity, Lower bounds, Order statistics
Persistent URL dx.doi.org/10.1016/j.ipl.2009.05.004
Journal Information Processing Letters
Citation
Mörig, M. (Marc), Rautenbach, D. (Dieter), Smid, M, & Tusch, J. (Jan). (2009). An Ω (n log n) lower bound for computing the sum of even-ranked elements. Information Processing Letters, 109(16), 955–956. doi:10.1016/j.ipl.2009.05.004