Approximating Rearrangement Distances with Replicas and Flexible Intergenic Regions

Abstract

Many tools from Computational Biology compute distances between genomes by counting the number of genome rearrangement events, such as reversals of a segment of genes. Most approaches to model these problems consider some simplifications such as ignoring nucleotides outside genes (the so-called intergenic regions), or assuming that just a single copy of each gene exists in the genomes. Recent works made advancements in more general models considering replicated genes and the number of nucleotides in intergenic regions. Our work aims at adapting those results by applying some flexibilization to match intergenic regions that do not have the same number of nucleotides. We propose the Signed Flexible Intergenic Reversal Distance problem, which seeks the minimum number of reversals necessary to transform one genome into the other and encodes the genomes using flexible intergenic region information while also allowing multiple copies of a gene. We show the relationship of this problem with the Signed Minimum Common Flexible Intergenic String Partition problem and use a 2k-approximation to the partition problem to show a 8k-approximation to the distance problem, where k is the maximum number of copies of a gene in the genomes.