Prefix Reversals on Binary and Ternary Strings

  • Cor Hurkens
  • Leo van Iersel
  • Judith Keijsper
  • Steven Kelk
  • Leen Stougie
  • John Tromp
Conference paper

DOI: 10.1007/978-3-540-73433-8_21

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4545)
Cite this paper as:
Hurkens C., van Iersel L., Keijsper J., Kelk S., Stougie L., Tromp J. (2007) Prefix Reversals on Binary and Ternary Strings. In: Anai H., Horimoto K., Kutsia T. (eds) Algebraic Biology. AB 2007. Lecture Notes in Computer Science, vol 4545. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Cor Hurkens
    • 1
  • Leo van Iersel
    • 1
  • Judith Keijsper
    • 1
  • Steven Kelk
    • 2
  • Leen Stougie
    • 1
    • 2
  • John Tromp
    • 2
  1. 1.Technische Universiteit Eindhoven (TU/e), Den Dolech 2, 5612 AX EindhovenNetherlands
  2. 2.Centrum voor Wiskunde en Informatica (CWI), Kruislaan 413, 1098 SJ AmsterdamNetherlands

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