Prefix Reversals on Binary and Ternary Strings

Given a permutation , the application of prefix reversal f(i) to reverses the order of the first i elements of . 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 ...

• Type: Conference
• Year: 2007
• Where: AB
• Authors: Cor A. J. Hurkens, Leo van Iersel, Judith Keijsper, Steven Kelk, Leen Stougie, John Tromp
• Keywords: AB 2007, Computational Biology, Prefix Reversal, Prefix Reversal Diameter, Ternary Strings