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.
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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.
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© 1990 Springer-Verlag Berlin Heidelberg
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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
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DOI: https://doi.org/10.1007/3-540-52282-4_43
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Online ISBN: 978-3-540-46945-2
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