Translocation is a prevalent rearrangement event in the evolution of multi-chromosomal species which exchanges ends between two chromosomes. A translocation is reciprocal if none of the exchanged ends is empty; otherwise, non-reciprocal. Given two signed multi-chromosomal genomes
, the problem of sorting by translocations is to find a shortest sequence of translocations transforming
. 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, for the first time, we study the problem of sorting by generalized translocations, which allows both reciprocal translocations and non-reciprocal translocations. We present an exact formula for computing the generalized translocation distance, which leads to a polynomial algorithm for this problem.