Approximate counting with m counters: A probabilistic analysis

Volume: 2 Number: 3 September 14, 2015
  • Guy Louchard
  • Helmut Prodinger
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

  1. 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.
  2. P. Flajolet and R. Sedgewick, Digital search trees revisited, SIAM J. Comput., 3, 748–767, 1986.
  3. M. Fuchs, C. K. Lee, and H. Prodinger, Approximate counting via the Poisson-Laplace-Mellin method, DMTCS, proc AQ, 13–28, 2012.
  4. 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.
  5. P. Kirschenhofer and H. Prodinger, Approximate counting: An alternative approach, RAIRO Theor. Inform. Appl., 25, 43–48, 1991.
  6. D. E. Knuth, The art of computer programming, volume 3: Sorting and searching, Addison-Wesley, 1973, (Second edition, 1998).
  7. M. Loève, Probability theory, 3rd ed, D. Van Nostrand, 1963.
  8. 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

-

Authors

Guy Louchard This is me

Helmut Prodinger This is me

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