2021/12/10 by Dan Alistarh, Alistarh, Dan, Peter Maxwell Davies +1
Mathematics · Physics and Astronomy · #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Parallel #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2112.05830
openalex publication_date 2021/12/10 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
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 pairwise interactions, during which they can exchange coupons. By doing so, they hope to reduce the number of coupons that must be sampled by each collector in order to obtain a full set. This extension is natural when considering real-world manifestations of the coupon collector phenomenon, and has been remarked upon and studied empirically [Hayes and Hannigan 2006, Ahmad et al. 2014, Delmarcelle 2019]. We provide the first theoretical analysis for such a scenario. We find that "coupon collecting with friends" can indeed significantly reduce the number of coupons each collector must sample, and raises interesting connections to the more traditional variants of the problem. While our analysis is in most cases asymptotically tight, there are several open questions raised, regarding finer-grained analysis of both "coupon collecting with friends", and of a long-studied variant of the original problem in which a collector requires multiple full sets of coupons.