Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference10 articles.
1. Some New Aspects of the Coupon Collector's Problem
2. Martingale approach to the coupon collection problem
3. Mitzenmacher M. D. (1996). The power of two choices in randomized load balancing. Doctoral Thesis, University of California, Berkeley.
4. Balanced Allocations
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