On the Complexity of Some Variations of Sorting by Transpositions

Author:

Alexandrino Alexsandro,Oliveira Andre,Dias Ulisses,Dias Zanoni

Abstract

One of the main challenges in Computational Biology is to find the evolutionary distance between two organisms. In the field of comparative genomics, one way to estimate such distance is to find a minimum cost sequence of rearrangements (large scale mutations) needed to transform one genome into another, which is called the rearrangement distance. In the past decades, these problems were studied considering many types of rearrangements (such as reversals, transpositions, transreversals, and revrevs) and considering the same weight for all rearrangements, or different weights depending on the types of rearrangements. The complexity of the problems involving reversals, transpositions, and both rearrangements is known, even though the hardness proof for the problem combining reversals and transpositions was recently given. In this paper, we enhance the knowledge for these problems by proving that models involving transpositions alongside reversals, transreversals, and revrevs are NP-hard, considering weights w1 for reversals and w2 for the other rearrangements such that w2/w1 ≤ 1.5. In addition, we address a cost function related to the number of fragmentations caused by a rearrangement, proving that the problem of finding a minimum cost sorting sequence, considering the fragmentation cost function with some restrictions, is NP-hard for transpositions and the combination of reversals and transpositions.

Publisher

Pensoft Publishers

Subject

General Computer Science,Theoretical Computer Science

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Rearrangement Distance Problems: An updated survey;ACM Computing Surveys;2024-04-26

2. Rearrangement Events on Circular Genomes;Bulletin of Mathematical Biology;2023-09-25

3. Approximation algorithms for sorting by k-cuts on signed permutations;Journal of Combinatorial Optimization;2022-11-17

4. Sorting by k-Cuts on Signed Permutations;Comparative Genomics;2022

5. Improved upper bound for sorting permutations by prefix transpositions;Theoretical Computer Science;2021-12

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