REVERSALS AND TRANSPOSITIONS OVER FINITE ALPHABETS

Authors

A. J. Radcliffe, University of Nebraska - LincolnFollow
A. D. Scott, University College LondonFollow
E. L. Wilmer, Oberlin CollegeFollow

Document Type

Article

Date of this Version

2005

Citation

SIAM J. DISCRETE MATH. Vol. 19, No. 1, pp. 224–244

Comments

Copyright 2005 Society for Industrial and Applied Mathematics

Abstract

Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition, or signed reversal distance between two strings over a finite alphabet is NP-hard, while for “dense” instances we give a polynomial-time approximation scheme. We also give a number of extremal results, as well as investigating the distance between random strings and the problem of sorting a string over a finite alphabet.