Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T13:55:11.607Z Has data issue: false hasContentIssue false
  • English
  • Français

The coupon subset collection problem

Part of: Combinatorial probability Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Ilan Adler  and
Sheldon M. Ross
Ilan Adler*
Affiliation:
University of California, Berkeley
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, 94720, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

The coupon subset collection problem is a generalization of the classical coupon collecting problem, in that rather than collecting individual coupons we obtain, at each time point, a random subset of coupons. The problem of interest is to determine the expected number of subsets needed until each coupon is contained in at least one of these subsets. We provide bounds on this number, give efficient simulation procedures for estimating it, and then apply our results to a reliability problem.

Keywords

Coupon collecting simulationcombinatorial probabilityboundsexchangeable caserandomly chosen subsetsreliability application

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 65C05: Monte Carlo methods
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 737 - 746
Copyright
Copyright © by the Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bosch, R. A. (2000). Optimal card-collecting strategies for magic: the gathering. College Math. J. 31, 15–21.Google Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, 3rd edn. John Wiley, Chichester.Google Scholar
Flajolet, P., Gardy, D., and Thimonier, L. (1992). Birthday paradox, coupon collectors, caching algorithms, and self-organizing search. Discrete Appl. Math. 39, 207–229.Google Scholar
Holst, L. (1986). On birthday, collectors', occupancy and other classical urn problems. Int. Statist. Rev. 54, 15–27.CrossRefGoogle Scholar
Peköz, E., and Ross, S. M. (1997). Estimating the mean cover time of a semi-Markov process via simulation. Prob. Eng. Inf. Sci. 11, 267–271.Google Scholar
Peköz, E., and Ross, S. M. (1999). Mean cover times for coupon collectors and star graphs. In Applied Probability and Stochastic Processes, eds Shanthikumar, J. G. and Sumita, U. Kluwer, Boston, pp. 83–94.Google Scholar
Stadje, W. (1990). The collector's problem with group drawings. Adv. Appl. Prob. 22, 866–874.Google Scholar