A new uniform translocation distance

Abstract

A basic problem in the area of combinatorial algorithms for genome evolution is to determine the minimum number of large scale evolutionary events (genome rearrangements) that transform a genome into another. The present paper is a contribution to the algorithmic study of genom evolution by translocations which is an area related to pattern recognition. Furthermore, it may be viewed as a contribution to other areas related to pattern recognition like: error estimation, genetic programming, disease diagnosis. In this paper we consider chromosomes as being linear strings that exchange each other prefixes in the translocation process. A new type of translocation distance between a pair of multi-chromosomal genomes is introduced; we examine the complexity of computing this distance in the case of uniform translocation, that is at each step the strings exchange prefixes of the same length. We present an exact polynomial algorithm based on the "greedy" strategy when the target set is a singleton while a 2-approximation algorithm is provided when considering arbitrary target sets. Some open problems are finally formulated. © Springer-Verlag 2004.