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UNO Gets Easier for a Single Player

  • Palash Dey
  • Prachi Goyal
  • Neeldhara Misra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8496)

Abstract

This work is a follow up to[2, FUN 2010], which initiated a detailed analysis of the popular game of UNO®. We consider the solitaire version of the game, which was shown to be NP-complete. In[2], the authors also demonstrate a \(n^{O(c^2)}\) 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.

Keywords

Reduction Rule Feasible Sequence Label Pair Popular Game Maximal Subsequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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    Demaine, E.D., Demaine, M.L., Uehara, R., Uno, T., Uno, Y.: UNO Is Hard, Even for a Single Player. In: Boldi, P. (ed.) FUN 2010. LNCS, vol. 6099, pp. 133–144. Springer, Heidelberg (2010)CrossRefGoogle Scholar
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Palash Dey
    • 1
  • Prachi Goyal
    • 1
  • Neeldhara Misra
    • 1
  1. 1.Indian Institute of ScienceBangaloreIndia

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