Issue |
RAIRO-Oper. Res.
Volume 57, Number 3, May-June 2023
Graphs, Combinatorics, Algorithms and Optimization
|
|
---|---|---|
Page(s) | 1045 - 1058 | |
DOI | https://doi.org/10.1051/ro/2023052 | |
Published online | 11 May 2023 |
Algorithms for the genome median under a restricted measure of rearrangement
1
Faculdade de Computação, Universidade Federal de Mato Grosso do Sul, Campo Grande, Brazil
2
Department of Mathematics, Paderborn University, Paderborn, Germany
3
Institute for Medical Biometry and Bioinformatics, University Hospital Düsseldorf, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
* Corresponding author: fabio.martinez@ufms.br; fabio.viduani@gmail.com
Received:
6
December
2022
Accepted:
9
April
2023
Ancestral reconstruction is a classic task in comparative genomics. Here, we study the genome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. The distance stands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of the breakpoint median that can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure called c4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of the c4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that the c4-distance is useful for the study the genome median problem, from theoretical and practical perspectives.
Mathematics Subject Classification: 90C10 / 90C27 / 90C35 / 90C59
Key words: Median problem / optimization / integer linear programming / heuristics
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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