EN
Approximate counting with m counters: A probabilistic analysis
Abstract
Motivated by a recent paper by Cicho\'n and Macyna [1], who introduced $m$ counters (instead of just one) in the approximate counting scheme first analysed by Flajolet [2], we analyse the moments of the sum of the $m$ counters, using techniques that proved to be successful already in several other contexts [11].
Keywords
References
- J. Cichoń and W. Macyna, Approximate counters for flash memory, 17th IEEE International Confer- ence on Embedded and Real-Time Computing Systems and Applications (RTCSA), Toyama, Japan, 20 P. Flajolet, Approximate counting: A detailed analysis, BIT, 25, 113–134, 1985.
- P. Flajolet and R. Sedgewick, Digital search trees revisited, SIAM J. Comput., 3, 748–767, 1986.
- M. Fuchs, C. K. Lee, and H. Prodinger, Approximate counting via the Poisson-Laplace-Mellin method, DMTCS, proc AQ, 13–28, 2012.
- H.-K. Hwang, M. Fuchs and V. Zacharovas, Asymptotic variance of random symmetric digital search trees, Discrete Math. Theor. Comput. Sci., 12, 103–166, 2010.
- P. Kirschenhofer and H. Prodinger, Approximate counting: An alternative approach, RAIRO Theor. Inform. Appl., 25, 43–48, 1991.
- D. E. Knuth, The art of computer programming, volume 3: Sorting and searching, Addison-Wesley, 1973, (Second edition, 1998).
- M. Loève, Probability theory, 3rd ed, D. Van Nostrand, 1963.
- G. Louchard, Exact and asymptotic distributions in digital and binary search trees, RAIRO Theor. Inform. Appl., 21(4), 479–496, 1987.
Details
Primary Language
English
Subjects
-
Journal Section
-
Publication Date
September 14, 2015
Submission Date
September 14, 2015
Acceptance Date
-
Published in Issue
Year 2015 Volume: 2 Number: 3
APA
Louchard, G., & Prodinger, H. (2015). Approximate counting with m counters: A probabilistic analysis. Journal of Algebra Combinatorics Discrete Structures and Applications, 2(3), 191-209. https://doi.org/10.13069/jacodesmath.36015
AMA
1.Louchard G, Prodinger H. Approximate counting with m counters: A probabilistic analysis. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2(3):191-209. doi:10.13069/jacodesmath.36015
Chicago
Louchard, Guy, and Helmut Prodinger. 2015. “Approximate Counting With M Counters: A Probabilistic Analysis”. Journal of Algebra Combinatorics Discrete Structures and Applications 2 (3): 191-209. https://doi.org/10.13069/jacodesmath.36015.
EndNote
Louchard G, Prodinger H (September 1, 2015) Approximate counting with m counters: A probabilistic analysis. Journal of Algebra Combinatorics Discrete Structures and Applications 2 3 191–209.
IEEE
[1]G. Louchard and H. Prodinger, “Approximate counting with m counters: A probabilistic analysis”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 2, no. 3, pp. 191–209, Sept. 2015, doi: 10.13069/jacodesmath.36015.
ISNAD
Louchard, Guy - Prodinger, Helmut. “Approximate Counting With M Counters: A Probabilistic Analysis”. Journal of Algebra Combinatorics Discrete Structures and Applications 2/3 (September 1, 2015): 191-209. https://doi.org/10.13069/jacodesmath.36015.
JAMA
1.Louchard G, Prodinger H. Approximate counting with m counters: A probabilistic analysis. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2:191–209.
MLA
Louchard, Guy, and Helmut Prodinger. “Approximate Counting With M Counters: A Probabilistic Analysis”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 2, no. 3, Sept. 2015, pp. 191-09, doi:10.13069/jacodesmath.36015.
Vancouver
1.Guy Louchard, Helmut Prodinger. Approximate counting with m counters: A probabilistic analysis. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015 Sep. 1;2(3):191-209. doi:10.13069/jacodesmath.36015