Pancake Flipping Is Hard

Abstract : Pancake Flipping is the problem of sorting a stack of pancakes of di erent sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to ip the pancakes above it (that is, to perform a pre x reversal). In the burnt variant, one side of each pancake is marked as burnt, and it is required to nish 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 for 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.
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Laurent Bulteau, Guillaume Fertin, Irena Rusu. Pancake Flipping Is Hard. Journal of Computer and System Sciences, Elsevier, 2015, 81 (8), pp.1556-1574. ⟨10.1016/j.jcss.2015.02.003⟩. ⟨hal-01053461⟩

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