Some upper and lower bounds on the coupon collector problem

Authors:
S. Shioda
Affiliations:
Urban Environment & Systems, Faculty of Engineering, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 5
Cited 4

Birthday paradox, coupon collectors, caching algorithms and self-organizing search

Discrete Applied Mathematics
General asymptotic estimates for the coupon collector problem

Journal of Computational and Applied Mathematics
Asymptotics for the random coupon collector problem

Journal of Computational and Applied Mathematics
Network support for IP traceback

IEEE/ACM Transactions on Networking (TON)
Some bounds on the coupon collector problem

Random Structures & Algorithms

A theoretical approach to parameter value selection of probabilistic packet marking for IP traceback

AINTEC '09 Asian Internet Engineering Conference
Self-test techniques for crypto-devices

IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Formal analysis of the effectiveness and predictability of random testing

Proceedings of the 19th international symposium on Software testing and analysis
The search for the laws of automatic random testing

Proceedings of the 28th Annual ACM Symposium on Applied Computing

Quantified Score

Hi-index	7.29

Visualization

Abstract

The classical coupon collector problem is closely related to probabilistic-packet-marking (PPM) schemes for IP traceback problem in the Internet. In this paper, we study the classical coupon collector problem, and derive some upper and lower bounds of the complementary cumulative distribution function (ccdf) of the number of objects (coupons) that one has to check in order to detect a set of different objects. The derived bounds require much less computation than the exact formula. We numerically find that the proposed bounds are very close to the actual ccdf when detecting probabilities are set to the values common to the PPM schemes.