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)


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.


Reduction Rule Feasible Sequence Label Pair Popular Game Maximal Subsequence 
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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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