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Simulating a Coupon Collector

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Cyber Security, Cryptology, and Machine Learning (CSCML 2022)

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

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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.

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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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University, 84105, Beer Sheva, Israel

    Dina Barak-Pelleg

  2. Departments of Mathematics and Computer Science, Ben-Gurion University, 84105, Beer Sheva, Israel

    Daniel Berend

Authors
  1. Dina Barak-Pelleg
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  2. Daniel Berend
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Correspondence to Dina Barak-Pelleg .

Editor information

Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Shlomi Dolev

  2. University of Maryland, College Park, MD, USA

    Jonathan Katz

  3. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Amnon Meisels

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07688-6

  • Online ISBN: 978-3-031-07689-3

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