Abstract
This paper contains two probabilistic results about merging two sorted lists of sizes n and m with n<m. We design a probabilistic algorithm which in the worst case is significantly faster than any deterministic one in the range 1.618<m/n≤3. We extend it into a simple general algorithm which performs well for any ratio m/n. In particular, for m/n>1.618 it is significantly faster than binary merge. We also prove an average case lower bound for a wide class of merging algorithms, when 1<m/n<\(\sqrt 2\)+1.
Supported by NSF Grant CCR85-13926
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
C. Christen (1978) Improving the bound on optimal merging, Proceedings of 19th FOCS, pp. 259–266.
C. Christen (1978) On the optimality of the straight merging algorithm, Publication 296, Dép. d'Info. et de Rech. Op., Université de Montréal.
V. Chvatal (1984) Probabilistic methods in graph theory, Annals of Operations Research 1, pp. 171–182.
F. K. Hwang and S. Lin (1971), Optimal merging of 2 elements with n elements, Acta Informatica 1, pp. 145–158.
F. K. Hwang and S. Lin (1972), A simple algorithm for merging two disjoint linearly ordered lists, SIAM J. of Comput. 1, pp. 31–39.
F. K. Hwang and D. N. Deutsch (1973) A class of merging algorithms, JACM, Vol. 20, No. 1, pp. 148–159.
D. E. Knuth (1973), The Art of Computer Programming, Volume 3: Sorting and Searching, Addison-Wesley.
G. K. Manacher (1979), Significant improvements to the Hwang-Ling merging algorithm, JACM, Vol. 26, No. 3, pp. 434–440.
P. K. Stockmeyer and F. F. Yao (1980) On the optimality of linear merge, SIAM J of Comput. 9, pp. 85–90.
A. Yao (1977), Probabilistic computations: Towards a unified mesure of complexity, Proc. 18th FOCS, pp. 222–227.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de la Vega, W.F., Kannan, S., Santha, M. (1990). Two probabilistic results on merging. In: Asano, T., Ibaraki, T., Imai, H., Nishizeki, T. (eds) Algorithms. SIGAL 1990. Lecture Notes in Computer Science, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52921-7_61
Download citation
DOI: https://doi.org/10.1007/3-540-52921-7_61
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52921-7
Online ISBN: 978-3-540-47177-6
eBook Packages: Springer Book Archive