Muthukrishnan S., Sahinalp S.C. (2002) An Improved Algorithm for Sequence Comparison with Block Reversals. In: Rajsbaum S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg
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 log2X), and hence, is near-linear. Trivial approach takes quadratic time and the best known previous algorithm for this problem takes time ω(X log3X).