An improved algorithm for sequence comparison with block reversals

Abstract

Given two sequences X and Y that are strings over some alphabet set, we consider the distance d(X, Y) between them defined to be minimum number of character replacements and block (substring) reversals needed to transform X to Y (or vice versa). This is the “simplest” sequence comparison problem we know of that allows natural block edit operations. Block reversals arise naturally in genomic sequence comparison; they are also of interest in matching music data. We present an improved algorithm for exactly computing the distance d(X, Y); it takes time O(|X| log2 |X|), and hence, is near-linear. Trivial approach takes quadratic time and the best known previous algorithm for this problem takes time Ω(|X| log3 |X|).