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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bafna, V., Pevzner, P.: Genome rearrangements and sorting by reversals. In: FOCS, pp. 148–157. IEEE (1993)
Berman, P., Hannenhalli, S., Karpinski, M.: 1.375-Approximation Algorithm for Sorting by Reversals. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 200–210. Springer, Heidelberg (2002)
Berman, P., Karpinski, M.: On Some Tighter Inapproximability Results (Extended Abstract). In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 200–209. Springer, Heidelberg (1999)
Chitturi, B., Fahle, W., Meng, Z., Morales, L., Shields, C.O., Sudborough, I., Voit, W.: An (18/11)n upper bound for sorting by prefix reversals. Theoretical Computer Science 410(36), 3372–3390 (2009)
Cibulka, J.: On average and highest number of flips in pancake sorting. Theoretical Computer Science 412(8-10), 822–834 (2011)
Cohen, D., Blum, M.: On the problem of sorting burnt pancakes. Discrete Applied Mathematics 61(2), 105–120 (1995)
Dweighter, H. American Mathematics Monthly, 82(1) (1975): (pseudonym of Goodman, J.E.)
Fischer, J., Ginzinger, S.: A 2-Approximation Algorithm for Sorting by Prefix Reversals. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 415–425. Springer, Heidelberg (2005)
Gates, W., Papadimitriou, C.: Bounds for sorting by prefix reversal. Discrete Mathematics 27(1), 47–57 (1979)
Hannenhalli, S., Pevzner, P.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. In: STOC, pp. 178–189. ACM (1995)
Heydari, M., Sudborough, I.: On Sorting by Prefix Reversals and the Diameter of Pancake Networks. In: Meyer auf der Heide, F., Rosenberg, A.L., Monien, B. (eds.) Heinz Nixdorf Symposium 1992. LNCS, vol. 678, pp. 218–227. Springer, Heidelberg (1993)
Heydari, M., Sudborough, I.: On the diameter of the pancake network. Journal of Algorithms 25(1), 67–94 (1997)
Labarre, A., Cibulka, J.: Polynomial-time sortable stacks of burnt pancakes. Theoretical Computer Science 412(8-10), 695–702 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bulteau, L., Fertin, G., Rusu, I. (2012). Pancake Flipping Is Hard. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-32589-2_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32588-5
Online ISBN: 978-3-642-32589-2
eBook Packages: Computer ScienceComputer Science (R0)