منابع مشابه
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 ...
متن کاملThe Generalized Coupon Collector Problem
Coupons are collected one at a time from a population containing n distinct types of coupon. The process is repeated until all n coupon have been collected and the total number of draws, Y , from the population is recorded. It is assumed that the draws from the population are independent and identically distributed (draws with replacement) according to a probability distribution X with the prob...
متن کاملOptimization results for a generalized coupon collector problem
We study in this paper a generalized coupon collector problem, which consists in analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we prove that the almost uniform distrib...
متن کاملOn Von Schelling Formula for the Generalized Coupon Collector Problem
The Coupon Collector Problem (CCP) is a totem pole in the field of combinatorial problems and has many implications in different domains, e.g., the exact Miss rate of LRU caches. In CCP, a set {1,..n}, n>1, of distinct objects (coupons, items...) is sampled with replacement by a collector. This random process, frequently labelled Independent Reference Model (IRM), is independent of all past eve...
متن کاملThe Coupon-Collector Problem Revisited
A standard combinatorial problem calls to cstlmate the expected number of purchases of coupons needed LO complete Ute collection of all possible m different types. Generalizing this problem. by letting lhe coupons be obtained with an arbitrary probability distribution. and considering other related processes, the problem has been found to model many practical siwations. The usefulness of lhis m...
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2011
ISSN: 0021-9002,1475-6072
DOI: 10.1239/jap/1324046020