Hanabi is NP-complete, even for cheaters who look at their cards

Jean Francois Baffier; Man Kwun Chiu; Santiago Diez Donoso; Cozzetti Matias Korman; Valia Mitsou; André Van Renssen; Marcel Roeloffzen; Yushi Uno

doi:10.4230/LIPIcs.FUN.2016.4

Hanabi is NP-complete, even for cheaters who look at their cards

Jean Francois Baffier, Man Kwun Chiu, Santiago Diez Donoso, Cozzetti Matias Korman, Valia Mitsou, André Van Renssen, Marcel Roeloffzen, Yushi Uno

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Citations (Scopus)

Abstract

This paper studies a cooperative card game called Hanabi from an algorithmic combinatorial game theory viewpoint. The aim of the game is to play cards from 1 to n in increasing order (this has to be done independently in c different colors). Cards are drawn from a deck one by one. Drawn cards are either immediately played, discarded or stored for future use (overall each player can store up to h cards). The main feature of the game is that players know the cards their partners hold (but not theirs. This information must be shared through hints). We introduce a simplified mathematical model of a single-player version of the game, and show several complexity results: the game is intractable in a general setting even if we forego with the hidden information aspect of the game. On the positive side, the game can be solved in linear time for some interesting restricted cases (i.e., for small values of h and c).

Original language	English
Title of host publication	8th International Conference on Fun with Algorithms, FUN 2016
Editors	Erik D. Demaine, Fabrizio Grandoni
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959770057
DOIs	https://doi.org/10.4230/LIPIcs.FUN.2016.4
Publication status	Published - 2016 Jun 1
Event	8th International Conference on Fun with Algorithms, FUN 2016 - La Maddalena, Italy Duration: 2016 Jun 8 → 2016 Jun 10

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	49
ISSN (Print)	1868-8969

Other

Other	8th International Conference on Fun with Algorithms, FUN 2016
Country	Italy
City	La Maddalena
Period	16/6/8 → 16/6/10

Keywords

Algorithmic combinatorial game theory
Sorting

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.FUN.2016.4

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Cite this

Baffier, J. F., Chiu, M. K., Diez Donoso, S., Korman, C. M., Mitsou, V., Van Renssen, A., Roeloffzen, M., & Uno, Y. (2016). Hanabi is NP-complete, even for cheaters who look at their cards. In E. D. Demaine, & F. Grandoni (Eds.), 8th International Conference on Fun with Algorithms, FUN 2016 [4] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 49). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.FUN.2016.4

Hanabi is NP-complete, even for cheaters who look at their cards. / Baffier, Jean Francois; Chiu, Man Kwun; Diez Donoso, Santiago; Korman, Cozzetti Matias; Mitsou, Valia; Van Renssen, André; Roeloffzen, Marcel; Uno, Yushi.

8th International Conference on Fun with Algorithms, FUN 2016. ed. / Erik D. Demaine; Fabrizio Grandoni. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016. 4 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 49).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Baffier, JF, Chiu, MK, Diez Donoso, S, Korman, CM, Mitsou, V, Van Renssen, A, Roeloffzen, M & Uno, Y 2016, Hanabi is NP-complete, even for cheaters who look at their cards. in ED Demaine & F Grandoni (eds), 8th International Conference on Fun with Algorithms, FUN 2016., 4, Leibniz International Proceedings in Informatics, LIPIcs, vol. 49, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 8th International Conference on Fun with Algorithms, FUN 2016, La Maddalena, Italy, 16/6/8. https://doi.org/10.4230/LIPIcs.FUN.2016.4

Baffier JF, Chiu MK, Diez Donoso S, Korman CM, Mitsou V, Van Renssen A et al. Hanabi is NP-complete, even for cheaters who look at their cards. In Demaine ED, Grandoni F, editors, 8th International Conference on Fun with Algorithms, FUN 2016. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2016. 4. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.FUN.2016.4

Baffier, Jean Francois ; Chiu, Man Kwun ; Diez Donoso, Santiago ; Korman, Cozzetti Matias ; Mitsou, Valia ; Van Renssen, André ; Roeloffzen, Marcel ; Uno, Yushi. / Hanabi is NP-complete, even for cheaters who look at their cards. 8th International Conference on Fun with Algorithms, FUN 2016. editor / Erik D. Demaine ; Fabrizio Grandoni. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2016. (Leibniz International Proceedings in Informatics, LIPIcs).

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