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

Jean-Francois Baffier; Man Kwun Chiu; Yago Diez; 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, Yago Diez, Matias Korman, Valia Mitsou, André van Renssen, Marcel Roeloffzen, Yushi Uno

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

6 Citations (Scopus)

185 Downloads (Pure)

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	E.D. Demaine, F. Grandoni
Place of Publication	Dagstuhl
Publisher	Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Number of pages	17
Volume	49
ISBN (Electronic)	9783959770057
DOIs	https://doi.org/10.4230/LIPIcs.FUN.2016.4
Publication status	Published - 1 Jun 2016
Externally published	Yes
Event	8th International Conference on Fun with Algorithms (FUN 2016) - La Maddalena, Italy Duration: 8 Jun 2016 → 10 Jun 2016 Conference number: 8

Publication series

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

Conference

Conference	8th International Conference on Fun with Algorithms (FUN 2016)
Abbreviated title	FUN 2016
Country/Territory	Italy
City	La Maddalena
Period	8/06/16 → 10/06/16

Keywords

Algorithmic combinatorial game theory
Sorting

Access to Document

10.4230/LIPIcs.FUN.2016.4

publishers versionFinal published version, 562 KBLicence: CC BY

Cite this

Baffier, J.-F., Chiu, M. K., Diez, Y., Korman, 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 (Vol. 49). Article 4 (Leibniz International Proceedings in Informatics (LIPIcs); Vol. 49). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FUN.2016.4

@inproceedings{4ef4adcbb19645b0b013877190a09e53,

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

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).",

keywords = "Algorithmic combinatorial game theory, Sorting",

author = "Jean-Francois Baffier and Chiu, {Man Kwun} and Yago Diez and Matias Korman and Valia Mitsou and {van Renssen}, Andr{\'e} and Marcel Roeloffzen and Yushi Uno",

year = "2016",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.FUN.2016.4",

language = "English",

volume = "49",

series = "Leibniz International Proceedings in Informatics (LIPIcs)",

publisher = "Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik",

editor = "E.D. Demaine and F. Grandoni",

booktitle = "8th International Conference on Fun with Algorithms, FUN 2016",

note = "8th International Conference on Fun with Algorithms (FUN 2016), FUN 2016 ; Conference date: 08-06-2016 Through 10-06-2016",

}

Baffier, J-F, Chiu, MK, Diez, Y, Korman, M, 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. vol. 49, 4, Leibniz International Proceedings in Informatics (LIPIcs), vol. 49, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, 8th International Conference on Fun with Algorithms (FUN 2016), La Maddalena, Italy, 8/06/16. 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, Yago et al.
8th International Conference on Fun with Algorithms, FUN 2016. ed. / E.D. Demaine; F. Grandoni. Vol. 49 Dagstuhl: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. 4 (Leibniz International Proceedings in Informatics (LIPIcs); Vol. 49).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Hanabi is NP-complete, even for cheaters who look at their cards

AU - Baffier, Jean-Francois

AU - Chiu, Man Kwun

AU - Diez, Yago

AU - Korman, Matias

AU - Mitsou, Valia

AU - van Renssen, André

AU - Roeloffzen, Marcel

AU - Uno, Yushi

N1 - Conference code: 8

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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).

AB - 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).

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DO - 10.4230/LIPIcs.FUN.2016.4

M3 - Conference contribution

AN - SCOPUS:84975263324

VL - 49

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

BT - 8th International Conference on Fun with Algorithms, FUN 2016

A2 - Demaine, E.D.

A2 - Grandoni, F.

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

CY - Dagstuhl

T2 - 8th International Conference on Fun with Algorithms (FUN 2016)

Y2 - 8 June 2016 through 10 June 2016

ER -

Baffier JF, Chiu MK, Diez Y, Korman M, 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. Vol. 49. Dagstuhl: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. 2016. 4. (Leibniz International Proceedings in Informatics (LIPIcs)). doi: 10.4230/LIPIcs.FUN.2016.4

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

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