Prefix reversals on binary and ternary strings

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dc.creatorHurkens, Cor
dc.creatorvan Iersel, Leo
dc.creatorKeijsper, Judith
dc.creatorKelk, Steven
dc.creatorStougie, Leen
dc.creatorTromp, John
dc.date2006-02-21
dc.date2006-07-04
dc.date.accessioned2026-07-07T07:03:38Z
dc.date.available2026-07-07T07:03:38Z
dc.descriptionGiven a permutation pi, the application of prefix reversal f^(i) to pi reverses the order of the first i elements of pi. 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.
dc.description20 pages. Just submitted for journal publication. Previous version should be considered no longer valid
dc.identifierhttps://arxiv.org/abs/math/0602456
dc.identifierhttp://arxiv.org/abs/math/0602456
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109049
dc.subjectCombinatorics
dc.subjectOptimization and Control
dc.titlePrefix reversals on binary and ternary strings
dc.typetext

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