With publication of the new study “Pancake Flipping is Hard” by three researchers at the University of Nantes, the city of Nantes becomes the de facto international capital of pancake research. Details of the study are given below. First, here is a Google map showing primary sources of pancakes in the city:
The study is:
“Pancake Flipping is Hard,” Laurent Bulteau, Guillaume Fertin [pictured here] and Irena Rusu, arXiv:1111.0434v1. (Submitted on 2 November 2011. (Thanks to Imke Fries for bringing this to our attention.) The authors report:
“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.”
Here is further detail— figure #10 from the study:
