A Generalized Coupon Collector Problem

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

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Weiyu Xu, Ao Kevin Tang
• Keywords: CORR 2010, Coupon Collector Problem, Coupons, Education, Efficient Exact Algorithm