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...

Based upon inequalities on Subset Probabilities, proofs of several conjectures on the Generalized Coupon Collector Problem (i.e. CCP with unequal popularity) are presented. Then we derive a very simple asymptotic relation between the expectation of the waiting time for a partial collection in the CCP, and the Miss rate of a LRU cache.

A multi-coupon (MC ) represents a collection of k coupons that a user can redeem to a vendor in exchange for a benefit (some good or service). Recently, Chen et al. [CEL07] proposed an unforgeable privacy-protecting multi-coupon scheme (MCS ), which discourages sharing of coupons through a property called unsplittability, where the coupons of a singleMC cannot be separately used by two users. P...

In this note we will consider the following problem: how many coupons we have to purchase (on average) to complete a collection. This problem, which takes everybody back to his childhood when this was really “a problem”, has been considered by the probabilists since the eighteenth century and nowadays it is still possible to derive some new results, probably original or at least never published...

We consider a generalized form of the coupon collection problem in which a random number, S, of balls is drawn at each stage from an urn initially containing n white balls (coupons). Each white ball drawn is colored red and returned to the urn; red balls drawn are simply returned to the urn. The question considered is then: how many white balls (uncollected coupons) remain in the urn after the ...

Hashing is one of the main techniques in data processing and algorithm design for very large data sets. While random hash functions satisfy most desirable properties, it is often too expensive to store a fully random hash function. Motivated by this, much attention has been given to designing small families of hash functions suitable for various applications. In this work, we study the question...

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 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...