Polynomial-time algorithm for computing translocation distance between genomes

With the advent of large-scale DNA physical mapping and sequencing, studies of genome rearrangements are becoming increasingly important in evolutionary molecular biology. From a computational perspective, the study of evolution based on rearrangements leads to a rearrangement distance problem, i.e., computing the minimum number of rearrangement events required to transform one genome into another. Different types of rearrangement events give rise to a spectrum of interesting combinatorial problems. The complexity of most of these problems is unknown. Multichromosomal genomes frequently evolve by a rearrangement event called translocation which exchanges genetic material between different chromosomes. In this paper we study the translocation distance problem, modeling the evolution of genomes evolving by translocations. The translocation distance problem was recently studied for the first time by Kececioglu and Ravi, who gave a 2-approximation algorithm for computing translocation distance. In this paper we prove a duality theorem leading to a polynomial time algorithm for computing translocation distance for the case when the orientations of the genes are known. This leads to an algorithm generating a most parsimonious (shortest) scenario, transforming one genome into another by translocations.