Abstract

Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the pancakes above it (that is, to perform a prefix reversal). In the burnt variant, one side of each pancake is marked as burnt, and it is required to finish with all pancakes having the burnt side down. Computing the optimal scenario for any stack of pancakes and determining the worst-case stack for any stack size have been challenges over more than three decades. Beyond being an intriguing combinatorial problem in itself, it also yields applications, e.g. in parallel computing and computational biology.

In this paper, we show that the Pancake Flipping problem, in its original (unburnt) variant, is NP-hard, thus answering the long-standing question of its computational complexity.

Keywords

Pancake problem Computational complexity Permutations Prefix reversals 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Laurent Bulteau
    • 1
  • Guillaume Fertin
    • 1
  • Irena Rusu
    • 1
  1. 1.Laboratoire d’Informatique de Nantes-Atlantique (LINA)UMR CNRS 6241, Université de NantesNantes Cedex 3France

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