Related papers: The clumsy coupon collector's problem
This paper provides analysis to a generalized version of the coupon collector problem, in which the collector gets $d$ distinct coupons each run and she chooses the one that she has the least so far. On the asymptotic case when the number…
This Ph.D. thesis concerns the version of the classical coupon collector's problem, when a collector samples with replacement a set of $n\ge 2$ distinct coupons so that at each time any one of the $n$ coupons is drawn with the same…
In this note, we introduce a distributed twist on the classic coupon collector problem: a set of $m$ collectors wish to each obtain a set of $n$ coupons; for this, they can each sample coupons uniformly at random, but can also meet in…
We consider an extended variant of the classical coupon collector's problem with infinite number of collections. An arriving coupon is placed in the $r^{th}$ collection, $r\ge0$, if $r$ is the smallest index such that the corresponding…
We initiate the study of the Careless Coupon Collector's Problem (CCCP), a novel variation of the classical coupon collector, that we envision as a model for information systems such as web crawlers, dynamic caches, and fault-resilient…
We consider a generalisation of the classical coupon collector problem. We define a super-coupon to be any $s$-subset of a universe of $n$ coupons. In each round, a random $r$-subset from the universe is drawn and all its $s$-subsets are…
A collector wishes to collect $m$ complete sets of $N$ distinct coupons. The draws from the population are considered to be independent and identical distributed with replacement, and the probability that a type-$j$ coupon is drawn is noted…
The Coupon Collector Problem (CCP) is a well-known combinatorial problem that seeks to estimate the number of random draws required to complete a collection of $n$ distinct coupon types. Various generalizations of this problem have been…
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…
We study in this paper a generalized coupon collector problem, which consists in determining the distribution and the moments of the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an…
Consider the coupon collector problem where each box of a brand of cereal contains a coupon and there are n different types of coupons. Suppose that the probability of a box containing a coupon of a specific type is $1/n$ and that we keep…
In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.
The "double Dixie cup problem" of D.J. Newman and L. Shepp (1960) is a well-known variant of the coupon collector's problem, where the object of study is the number $T_{m}(N)$ of coupons that a collector has to buy in order to complete $m$…
A popular variant of the collector's problem is the following: Assume there are $N$ different types of coupons with equal occurring probabilities. There is one main collector who collects coupons. When she gets a "double," she gives it to…
We generalize the well-known Coupon Collector Problem (CCP) in combinatorics. Our problem is to find the minimum and expected number of draws, with replacement, required to recover $n$ distinctly labeled coupons, with each draw consisting…
We extend the classical coupon collector's problem to one in which two collectors are simultaneously and independently seeking collections of $d$ coupons. We find, in finite terms, the probability that the two collectors finish at the same…
Motivated by applications in bioinformatics, we consider the word collector problem, i.e. the expected number of calls to a random weighted generator of words of length $n$ before the full collection is obtained. The originality of this…
In this note we evaluate the expected waiting time to complete a collection of coupons, in the case of coupons which arrives in groups of constant size, independently and with unequal probabilities. As an application we will be able to…
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to…
The following variant of the collector's problem has attracted considerable attention relatively recently (see, e.g., N. Pintacuda 1980, D. Foata H. Guo-Niu and B. Lass 2001, D. Foata and D. Zeilberger 2003, I. Adler, S. Oren and S. Ross…