Efficient Generation of a Card-Based Uniformly Distributed Random Derangement

Soma Murata, Daiki Miyahara, Takaaki Mizuki, Hideaki Sone

研究成果: Conference contribution

抄録

Consider a situation, known as Secret Santa, where n players wish to exchange gifts such that each player receives exactly one gift and no one receives a gift from oneself. Each player only wants to know in advance for whom he/she should purchase a gift. That is, the players want to generate a hidden uniformly distributed random derangement. (Note that a permutation without any fixed points is called a derangement.) To solve this problem, in 2015, Ishikawa et al. proposed a simple protocol with a deck of physical cards. In their protocol, players first prepare n piles of cards, each of which corresponds to a player, and shuffle the piles. Subsequently, the players verify whether the resulting piles have fixed points somehow: If there is no fixed point, the piles serve as a hidden random derangement; otherwise, the players restart the shuffle process. Such a restart occurs with a probability of approximately 0.6. In this study, we consider how to decrease the probability of the need to restart the shuffle based on the aforementioned protocol. Specifically, we prepare more piles of cards than the number n of players. This potentially helps us avoid repeating the shuffle, because we can remove fixed points even if they arise (as long as the number of remaining piles is at least n). Accordingly, we propose an efficient protocol that generates a uniformly distributed random derangement. The probability of the need to restart the shuffle can be reduced to approximately 0.1.

本文言語English
ホスト出版物のタイトルWALCOM
ホスト出版物のサブタイトルAlgorithms and Computation - 15th International Conference and Workshops, WALCOM 2021, Proceedings
編集者Ryuhei Uehara, Seok-Hee Hong, Subhas C. Nandy
出版社Springer Science and Business Media Deutschland GmbH
ページ78-89
ページ数12
ISBN(印刷版)9783030682101
DOI
出版ステータスPublished - 2021
イベント15th International Conference on Algorithms and Computation, WALCOM 2021 - Virtual, Online
継続期間: 2021 2 282021 3 2

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
12635 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference15th International Conference on Algorithms and Computation, WALCOM 2021
CityVirtual, Online
Period21/2/2821/3/2

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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