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...

Consider the classical coupon-collector's problem in which items of m distinct types arrive in sequence. An arriving item is installed in system i > 1 if i is the smallest index such that system i does not contain an item of the arrival's type. We study the expected number of items in system j at the moment when system 1 first contains an item of each type.

Tournament selection performs tournaments by first sampling individuals uniformly at random from the population and then selecting the best of the sample for some genetic operation. This sampling process needs to be repeated many times when creating a new generation. However, even upon iteration, it may happen not to sample some of the individuals in the population. These individuals can theref...

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 instance of the non-uniform coupon collector lies in the, potentially large, multiplicity of the words/coupons of a given probability/composition. We obtain a gen...

We extend the classical coupon collector problem to find the expected number of selections needed to collect mi (possible random) copies of coupon i, when the distribution of the coupons is not necessarily equally likely. Upper and lower bounds which provide limiting asymptotics are also obtained for the expected number of selections needed to fulfill a random quota for each coupon.

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...

Coupons are collected one at a time from a population containing n distinct types of coupon. The process is repeated until all n coupons 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 distributionXwith the proba...

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 ...