On the problem of sorting burnt pancakes
Discrete Applied Mathematics
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
To cut…or not to cut (applications of comparative physical maps in molecular evolution)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
1.375-Approximation Algorithm for Sorting by Reversals
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Advances on sorting by reversals
Discrete Applied Mathematics
Genome rearrangements and sorting by reversals
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Edit Distances and Factorisations of Even Permutations
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics
Combinatorics of Genome Rearrangements
Combinatorics of Genome Rearrangements
A 2-approximation algorithm for sorting by prefix reversals
ESA'05 Proceedings of the 13th annual European conference on Algorithms
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
The distribution of cycles in breakpoint graphs of signed permutations
Discrete Applied Mathematics
| Hi-index | 5.23 |
Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses the order of the first k elements of the permutation. The burnt variant of pancake flipping involves permutations of signed integers, and reversals in that case not only reverse the order of elements but also invert their signs. Although three decades have now passed since the first works on these problems, neither their computational complexity nor the maximal number of prefix reversals needed to sort a permutation is yet known. In this work, we prove a new lower bound for sorting burnt pancakes, and show that an important class of permutations, known as ''simple permutations'', can be optimally sorted in polynomial time.