相关论文: Collecting Coupons is Faster with Friends

The solution of the classical Coupon Collector's Problem is based on the assumptions that all stickers are independently and uniformly distributed. We can prove statistically as well as analytically that in particular the assumption of…

We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the…

This paper gives an algebraic proof of the correctness of Von Schelling formula for the probability of the coupon collector problem waiting time for non-uniform distributions and partial collections. It introduces a theorem on sums of…

The Coupon Collector's Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no…

We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…

Despite the coupon collector's problem has simple probabilistic solution using inclusion/exclusion principle \cite{PolyaUrn}, starting from a particular type of recurrence differential equation it is used an analytic approach to recover…

Given a set of coins arranged in a line, we remove heads-up coins one at a time and flip any adjacent coins after each removal. The coin-removal problem is to determine for which arrangements of coins it is possible to remove all of the…

We study the two-player coupon-collector competition in which two independent collectors draw one coupon each per round from a set of $d$ equally likely coupon types. Myers and Wilf gave finite formulae for several two-player events and…

We describe a very simple method for `consistent sampling' that allows for sampling with replacement. The method extends previous approaches to consistent sampling, which assign a pseudorandom real number to each element, and sample those…

This note describes an algorithm for enumerating all the elements in a finite set based on uniformly random sampling from the set. This algorithm can be used for enumeration by fair sampling with quantum annealing. Our algorithm is based on…

Online electronic coupon (e-coupon) is becoming a primary tool for e-commerce platforms to attract users to place orders. E-coupons are the digital equivalent of traditional paper coupons which provide customers with discounts or gifts. One…

Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…

We study the coupon collector with deterministic expiration: one coupon is drawn at each time, and each coupon remains active for exactly $M$ draws. Completion occurs when all $n$ coupon types are simultaneously active. Equivalently, the…

We consider a model where an agent has a repeated decision to make and wishes to maximize their total payoff. Payoffs are influenced by an action taken by the agent, but also an unknown state of the world that evolves over time. Before…

Exploration is a fundamental problem in robotics. While sampling-based planners have shown high performance, they are oftentimes compute intensive and can exhibit high variance. To this end, we propose to directly learn the underlying…

Public opinion polling is usually done by random sampling from the entire population, treating individual opinions as independent. In the real world, individuals' opinions are often correlated, e.g., among friends in a social network. In…

Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…

In many real life situations one has $m$ types of random events happening in chronological order within a time interval and one wishes to predict various milestones about these events or their subsets. An example is birdwatching. Suppose we…

A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…

In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported…