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A003075
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Minimal number of comparisons needed for n-element sorting network.
(Formerly M2446)
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6
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0, 1, 3, 5, 9, 12, 16, 19, 25, 29, 35, 39
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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It is conjectured that the sequence continues (after 39) 45, 51, 56, 60, ...
a(13) <= 45 is mentioned in Knuth, Sorting and Searching, Vol. 2. a(9) was determined in 1991. - Ed Pegg Jr, Dec 05 2001.
Correction: the value for a(9) was not determined in the 1991 reference, which instead is about optimal depth. - Michael Codish, Jun 01 2014
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REFERENCES
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R. W. Floyd and D. E. Knuth, The Bose-Nelson sorting problem, pp. 163-172 of J. N. Srivastava, ed., A Survey of Combinatorial Theory, North-Holland, 1973.
H. Jullie, Lecture Notes in Comp. Sci. 929 (1995), 246-260.
D. E. Knuth, Art of Computer Programming, Vol. 3, Sect. 5.3.4, Eq. (11).
I. Parberry, "A Computer Assisted Optimal Depth Lower Bound for Nine-Input Sorting Networks", Mathematical Systems Theory, Vol. 24, pp. 101-116, 1991.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..12.
D. Bundala, M. Codish, L. Cruz-Filipe et al., Optimal-Depth Sorting Networks, arXiv preprint arXiv:1412.5302 [cs.DS], 2014.
Michael Codish, Luís Cruz-Filipe, Michael Frank, Peter Schneider-Kamp, Twenty-Five Comparators is Optimal when Sorting Nine Inputs (and Twenty-Nine for Ten), arXiv:1405.5754 [cs.DM], 2014.
Bert Dobbelaere, Smallest and fastest sorting networks for a given number of inputs
Milton W. Green, Letter to N. J. A. Sloane, 1973.
Jannis Harder, Lower Size Bounds for Sorting Networks
Mariana Nagy, Vlad-Florin Drăgoi, Valeriu Beiu, Employing Sorting Nets for Designing Reliable Computing Nets, IEEE 20th International Conference on Nanotechnology (IEEE-NANO 2020) 370-375.
Ian Parberry, A Computer Assisted Optimal Depth Lower Bound for Nine-Input Sorting Networks
Ed Pegg Jr., Illustration of initial terms
Index entries for sequences related to sorting
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CROSSREFS
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A006282 is an upper bound. Cf. A036604, A067782 (minimal depth).
Sequence in context: A191403 A233779 A287105 * A061562 A006282 A086845
Adjacent sequences: A003072 A003073 A003074 * A003076 A003077 A003078
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KEYWORD
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hard,nonn,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Updates from Ed Pegg Jr, Dec 05 2001
Correction and update: terms are exact for n<=10. The precise values for n=9 and n=10 are established in the reference from 2014 by Codish et al. - Michael Codish, Jun 01 2014
Entry revised by N. J. A. Sloane, Jun 02 2014
a(11)-a(12) from Jannis Harder, Dec 10 2019
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STATUS
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approved
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