On the problem of sorting burnt pancakes
Discrete Applied Mathematics
On the diameter of the pancake network
Journal of Algorithms
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Sorting Strings by Reversals and by Transpositions
SIAM Journal on Discrete Mathematics
Comparing star and pancake networks
The essence of computation
Reversals and Transpositions Over Finite Alphabets
SIAM Journal on Discrete Mathematics
Assignment of Orthologous Genes via Genome Rearrangement
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A 2-approximation algorithm for sorting by prefix reversals
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Sorting by weighted reversals, transpositions, and inverted transpositions
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
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Given a permutation π, the application of prefix reversal f(i) to π reverses the order of the first i elements of π. The problem of Sorting By Prefix Reversals (also known as pancake flipping), made famous by Gates and Papadimitriou (Bounds for sorting by prefix reversal, Discrete Mathematics 27, pp. 47-57), asks for the minimum number of prefix reversals required to sort the elements of a given permutation. In this paper we study a variant of this problem where the prefix reversals act not on permutations but on strings over a fixed size alphabet. We determine the minimum number of prefix reversals required to sort binary and ternary strings, with polynomial-time algorithms for these sorting problems as a result; demonstrate that computing the minimum prefix reversal distance between two binary strings is NP-hard; give an exact expression for the prefix reversal diameter of binary strings, and give bounds on the prefix reversal diameter of ternary strings. We also consider a weaker form of sorting called grouping (of identical symbols) and give polynomial-time algorithms for optimally grouping binary and ternary strings. A number of intriguing open problems are also discussed.