A003075 Minimal number of comparisons needed for n-element sorting network.
0, 1, 3, 5, 9, 12, 16, 19, 25, 29, 35, 39
Offset: 1
References
- 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).
Links
- 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 and 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 (note "A360" refers to N0360 which is A000788).
- Jannis Harder, Lower Size Bounds for Sorting Networks
- Mariana Nagy, Vlad-Florin Drăgoi and 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
Extensions
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
Comments