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A Generalized Coupon Collector Problem

Part of: Stochastic processes Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Weiyu Xu  and
A. Kevin Tang
Weiyu Xu*
Affiliation:
Cornell University
A. Kevin Tang*
Affiliation:
Cornell University
*
∗ Postal address: School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853, USA.
∗ Postal address: School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853, USA.
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Abstract

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This paper presents an analysis of a generalized version of the coupon collector problem, in which the collector receives d coupons each run and chooses the least-collected coupon so far. In the asymptotic case when the number of coupons n goes to infinity, we show that, on average, (nlogn) / d + (n / d)(m − 1)log logn + O(mn) runs are needed to collect m sets of coupons. An exact algorithm is also developed for any finite case to compute the exact mean number of runs. Numerical examples are provided to verify our theoretical predictions.

Keywords

Coupon collector problemexpected runstate-space representationwireless communicationopportunistic scheduling

MSC classification

Secondary: 60G70: Extreme value theory; extremal processes 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 1081 - 1094
Copyright
Copyright © Applied Probability Trust 2011 

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