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UNO Gets Easier for a Single Player

Dey, Palash and Goyal, Prachi and Misra, Neeldhara (2014) UNO Gets Easier for a Single Player. In: 7th International Conference on Fun with Algorithms, JUL 01-03, 2014, ITALY, pp. 147-157.

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Official URL: http://dx.doi.org/ 10.1007/978-3-319-07890-8_13

Abstract

This work is a follow up to 2, FUN 2010], which initiated a detailed analysis of the popular game of UNO (R). We consider the solitaire version of the game, which was shown to be NP-complete. In 2], the authors also demonstrate a (O)(n)(c(2)) algorithm, where c is the number of colors across all the cards, which implies, in particular that the problem is polynomial time when the number of colors is a constant. In this work, we propose a kernelization algorithm, a consequence of which is that the problem is fixed-parameter tractable when the number of colors is treated as a parameter. This removes the exponential dependence on c and answers the question stated in 2] in the affirmative. We also introduce a natural and possibly more challenging version of UNO that we call ``All Or None UNO''. For this variant, we prove that even the single-player version is NP-complete, and we show a single-exponential FPT algorithm, along with a cubic kernel.

Item Type: Conference Proceedings
Additional Information: Copy right for this article belongs to the SPRINGER-VERLAG BERLIN, HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 14 Nov 2014 07:29
Last Modified: 14 Nov 2014 07:29
URI: http://eprints.iisc.ac.in/id/eprint/50282

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