Polynomial-Time Algorithm for Sorting Genomes by Generalized Translocations

Sorting genomes by translocations plays an important role in the research of genome rearrangement.Translocation is a prevalent rearrangement event in the evolution of multi-chromosomal species which exchanges ends between two chromosomes.Translocations include reciprocal translocations and non-reciprocal translocations.Translocation sorting problem asks to find a shortest sequence of translocations to transform one genome into another.Several polynomial algorithms have been presented,all of them only allowing reciprocal translocations.Thus they can only be applied to a pair of genomes having the same set of chromosome ends.Such a restriction can be removed if non-reciprocal translocations are also allowed.In this paper,the authors study for the problem of sorting by generalized translocations,which allows both reciprocal and non-reciprocal translocations,and present a polynomial-time algorithm for this problem,in which the problem of sorting by generalized translocations is reduced in linear time to the problem of sorting by reciprocal translocations.This algorithm confirms Ozery-Flato's conjecture that sorting by generalized translocations could be solved in polynomial time.