Abstract
Given an ordered set ofn elements whose order is not known to us, it is shown that by making slightly more thancn 3/2 simultaneous comparison almost all comparisons can be deduced by direct implications. It is also shown that this result is essentially best possible, and that ifn is large, almost any choice ofcn 3/2 comparisons will yield almost all comparisons by direct implications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. E. Batcher,Sorting networks and their applications, Notices Amer. Math. Soc.14 (1967), 283.
B. Bollobás,Extremal Graph Theory, London Math. Soc. Monographs, Vol. 11, Academic Press, London-New York-San Francisco, 1978.
B. BollobásGraph Theory — An Introductory Course, Graduate Texts in Maths.63, Springer-Verlag, New York-Heidelberg, 1979.
P. Erdös and A. Rényi,On a problem in the theory of graphs, Publ. Math. Inst. Hungar. Acad. Sci.7 (1962), 215–235 (in Hungarian).
R. W. Floyd and D. E. Knuth,The Bose-Nelson sorting problem, a survey of combinatorial theory (Srivastava et al., eds.), North-Holland Publ. Co., 1973, pp. 163–172.
Roland Häggkvist and Pavol Hell,Parallel sorting with constant time for comparisons, SIAM J. Comput., to appear.
D. E. Knuth,The Art of Computer Programming, Vol. 3,Sorting and Searching, Addison-Wesley, Reading, Mass., 1973.
D. Van Voorhis,An Improved Lower Bound for the Bose-Nelson Sorting Problem, Technical Report No. 7, Digital Systems Laboratory, Stanford University, 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bollobás, B., Rosenfeld, M. Sorting in one round. Israel J. Math. 38, 154–160 (1981). https://doi.org/10.1007/BF02761857
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02761857