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UNO Is Hard, Even for a Single Player

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Fun with Algorithms (FUN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6099))

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Abstract

UNO\(\mbox{}^{\scriptsize\textregistered}\) is one of the world-wide well-known and popular card games. We investigate UNO from the viewpoint of combinatorial algorithmic game theory by giving some simple and concise mathematical models for it. They include cooperative and uncooperative versions of UNO, for example. As a result of analyzing their computational complexities, we prove that even a single-player version of UNO is NP-complete, while it becomes in P in some restricted cases. We also show that uncooperative two-player’s version is PSPACE-complete.

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Author information

Authors and Affiliations

  1. MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA

    Erik D. Demaine & Martin L. Demaine

  2. School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa, 923-1292, Japan

    Ryuhei Uehara

  3. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Takeaki Uno

  4. Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, 599-8531, Japan

    Yushi Uno

Authors
  1. Erik D. Demaine
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  2. Martin L. Demaine
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  3. Ryuhei Uehara
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  4. Takeaki Uno
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  5. Yushi Uno
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Editor information

Editors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, 20135, Milano, Italy

    Paolo Boldi

  2. Dip. di Informatica ed Applicazioni, Universitá di Salerno, 84084, Fisciano, Italy

    Luisa Gargano

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© 2010 Springer-Verlag Berlin Heidelberg

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Demaine, E.D., Demaine, M.L., Uehara, R., Uno, T., Uno, Y. (2010). UNO Is Hard, Even for a Single Player. In: Boldi, P., Gargano, L. (eds) Fun with Algorithms. FUN 2010. Lecture Notes in Computer Science, vol 6099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13122-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-13122-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13121-9

  • Online ISBN: 978-3-642-13122-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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