Pancake Flipping is hard

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 p...

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Bibliographic Details
Published inJournal of computer and system sciences Vol. 81; no. 8; pp. 1556 - 1574
Main Authors Bulteau, Laurent, Fertin, Guillaume, Rusu, Irena
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2015
Elsevier
Subjects
Bioinformatics
Computational Complexity
Computer Science
Life Sciences
Pancake problem
Permutations
Prefix reversals
Quantitative Methods
Permutations
Pancake problem
Prefix reversals
Computational complexity
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Summary: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 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.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2015.02.003