Abstract
Let (xi)1≤i≤n and (yj)1≤i≤n be two sequences of numbers. It was proved by M.L. Fredman in [1] that the n2 sums (xi+yj)1≤i,j≤n can be sorted in O(n2) comparisons, but until now, no explicit algorithm was known to do it. We present such an algorithm and generalize it to sort \((x_{i_1 }^1 + ... + x_{i_k }^k )1 \leqslant i_1 ,...i_k \leqslant n\) in O(nk) comparisons.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
M.L. Fredman, How good is the information theory about sorting?, Theoretical Computer Science 1 (1976) 355–361.
L.H. Harper, T.H. Payne, J.E. Savage, E. Straus, Sorting X+Y, Comm. ACM, June 1975, Volume 18, Number 6, 347–349.
N.Jacobson, "Basic algebra I", W.H.Freeman and company, 1974.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lambert, JL. (1990). Sorting the sums (xi+yj) in O(n2) comparisons. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_43
Download citation
DOI: https://doi.org/10.1007/3-540-52282-4_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52282-9
Online ISBN: 978-3-540-46945-2
eBook Packages: Springer Book Archive