Variações do Problema de Distância de Rearranjos (2404.17996v2)

Abstract: Considering a pair of genomes, the goal of rearrangement distance problems is to estimate how distant these genomes are from each other based on genome rearrangements. Seminal works in genome rearrangements assumed that both genomes being compared have the same set of genes (balanced genomes) and, furthermore, only the relative order of genes and their orientations, when they are known, are used in the mathematical representation of the genomes. In this case, the genomes are represented as permutations, originating the Sorting Permutations by Rearrangements problems. The main problems of Sorting Permutations by Rearrangements considered DCJs, reversals, transpositions, or the combination of both reversals and transpositions, and these problems have their complexity known. Besides these problems, other ones were studied involving the combination of transpositions with one or more of the following rearrangements: transreversals, revrevs, and reversals. Although there are approximation results for these problems, their complexity remained open. Some of the results of this thesis are the complexity proofs for these problems. Furthermore, we present a new 1.375-approximation algorithm, which has better time complexity, for the Sorting Permutations by Transpositions. When considering unbalanced genomes, it is necessary to use insertions and deletions to transform one genome into another. In this thesis, we studied Rearrangement Distance problems on unbalanced genomes considering only gene order and their orientations (when they are known), as well as Intergenic Rearrangement Distance problems, which incorporate the information regarding the size distribution of intergenic regions, besides the use of gene order and their orientations (when they are known). We present complexity proofs and approximation algorithms for problems that include reversals and transpositions.