Abstract
We use several statistics on digital search trees (tries) to analyze in detail an almost optimal algorithm for generating an exponentially distributed variate. The algorithm, based on ideas of J. von Neumann, is due to Knuth and Yao. We establish that it can generate k bits of an exponentially distributed variate in about k+5.67974692 coin flippings. This result is presented together with companion estimates on the distribution of costs; it answers an open problem of Knuth and Yao.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
P. FLAJOLET, D. SOTTEAU "A recursive partitionning process of computer science" in II World Conference on Mathematics at the Service of Man, Las Palmas (1982), pp. 25–30.
D.E. KNUTH "The Art of Computer Programming" Vol. 3 Sorting and Searching, Addison Wesley, Reading 1973.
D.E. KNUTH, A.C. YAO "The complexity of nonuniform random number generation" in Algorithms and Complexity, Academic Press, New-York (1976).
J. VON NEUMANN "Various techniques used in connection with random digits" notes by G.E. Forsythe, National Bureau of Standards, Applied Math Series, 12 (1951). Reprinted in Von Neumann's Collected Works 5 (Pergamon Press, 1963), pp. 768–770.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Flajolet, P., Saheb, N. (1983). Digital search trees and the generation of an exponentially distributed variate. In: Ausiello, G., Protasi, M. (eds) CAAP'83. CAAP 1983. Lecture Notes in Computer Science, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12727-5_13
Download citation
DOI: https://doi.org/10.1007/3-540-12727-5_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12727-7
Online ISBN: 978-3-540-38714-5
eBook Packages: Springer Book Archive