Exact and approximation algorithms for the contiguous translocation distance problem

Biological computation is the field that studies the computations performed by the biological systems and includes the development of algorithms or other computational techniques inspired by nature. The genome rearrangements that occur during genome evolution are an important example of a natural computation process which inspired multiple problems that can be solved using combinatorial models. A popular problem inspired by genome evolution is computing the genetic distance between two organisms by identifying the minimum number of genome rearrangements needed to obtain one genome from the other. Given two chromosomes, represented as strings over the DNA alphabet {A, C, G, T}, the translocation operation is defined as a prefix interchange between these chromosomes. Thus, two new chromosomes are obtained after a translocation. When the chromosomes are interchanging equal length prefixes, the translocation operation is called uniform. A translocation sequence is a series of translocation operations applied to an initial genome, represented as a set of strings (initial set), resulting in a new genome, also represented as a set of strings (target set). Given a translocation sequence, if the strings exchanging prefixes are part of the initial set or have additional copies created by preceding translocations than those utilised, then the translocation sequence is referred to as contiguous. The translocation distance between two given genomes is defined as the minimum number of translocation operations necessary to obtain one genome from the other. We introduce a new polynomial time exact algorithm to compute the uniform contiguous translocation distance for a target genome of size two. Then, we present a polynomial time 2-approximation algorithm for the non-uniform contiguous translocation distance considering a target genome of size one.