On the problem of sorting burnt pancakes
Discrete Applied Mathematics
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On the diameter of the pancake network
Journal of Algorithms
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
On Sorting by Prefix Reversals and the Diameter of Pancake Networks
Proceedings of the First Heinz Nixdorf Symposium on Parallel Architectures and Their Efficient Use
1.375-Approximation Algorithm for Sorting by Reversals
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Genome rearrangements and sorting by reversals
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
An (18/11)n upper bound for sorting by prefix reversals
Theoretical Computer Science
On average and highest number of flips in pancake sorting
Theoretical Computer Science
Polynomial-time sortable stacks of burnt pancakes
Theoretical Computer Science
A 2-approximation algorithm for sorting by prefix reversals
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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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.