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Simulating a Coupon Collector

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13301)

Abstract

The coupon collector’s problem (CCP) reads as follows: How many drawings are needed on average in order to complete a collection of n types of coupons, if at each step a single coupon is drawn uniformly randomly, independently of all the other drawings?

Since CCP was first introduced, numerous questions have been posed on its basis, and it also turned out to appear in many applications, such as DDoS cyber attacks and machine learning. It is well known that, in CCP, the convergence of various quantities of interest to their asymptotic values is rather slow. Thus, simulating the process to get a feeling for their behavior is often impractical.

We present here an alternative view of the process, which allows us, for equally probable coupons, to perform fast simulation for large values of the parameters.

Keywords

  • Coupon collector’s problem
  • Simulation

Research supported in part by the Milken Families Foundation Chair in Mathematics and the Cyber Security Research Center at Ben-Gurion University.

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Correspondence to Dina Barak-Pelleg .

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Barak-Pelleg, D., Berend, D. (2022). Simulating a Coupon Collector. In: Dolev, S., Katz, J., Meisels, A. (eds) Cyber Security, Cryptology, and Machine Learning. CSCML 2022. Lecture Notes in Computer Science, vol 13301. Springer, Cham. https://doi.org/10.1007/978-3-031-07689-3_5

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  • DOI: https://doi.org/10.1007/978-3-031-07689-3_5

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