Mixed and Circular Multichromosomal Genomic Median Problem

et al. 2020

Algorithms Mol Biol

Background. In the field of genome rearrangement algorithms, models accounting for gene duplication lead often to hard problems. For example, while computing the pairwise distance is tractable in most duplication-free models, the problem is NP-complete for most extensions of these models accounting for duplicated genes. Moreover, problems involving more than two genomes, such as the genome median and the Small Parsimony problem, are intractable for most duplication-free models, with some exceptions, for example the Single-Cut-or-Join (SCJ) model. Results. We introduce a variant of the SCJ distance that accounts for duplicated genes, in the context of directed evolution from an ancestral genome to a descendant genome where orthology relations between ancestral genes and their descendant are known. Our model includes two duplication mechanisms: single-gene tandem duplication and the creation of single-gene circular chromosomes. We prove that in this model, computing the directed distance and a parsimonious evolutionary scenario in terms of SCJ and single-gene duplication events can be done in linear time. We also show that the directed median problem is tractable for this distance, while the rooted median problem, where we assume that one of the given genomes is ancestral to the median, is NP-complete. We also describe an Integer Linear Program for solving this problem. We evaluate the directed distance and rooted median algorithms on simulated data. Conclusion. Our results provide a simple genome rearrangement model, extending the SCJ model to account for single-gene duplications, for which we prove a mix of tractability and hardness results. For the NP-complete rooted median problem, we design a simple Integer Linear Program. Our publicly available implementation of these algorithms for the directed distance and median problems allow to solve efficiently these problems on large instances.

Section: Algorithms For Molecular Biologymentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

The distance and median problems in the single-cut-or-join model with single-gene duplications

et al. 2020

Algorithms Mol Biol

“…However, in 2009, Tannier, Zheng and Sankoff proved that computing a median gene order that is allowed to contain an arbitrary mixture of linear and circular chromosomes was tractable in the breakpoint distance model, by using a reduction to the problem of computing a Maximum Weight Matching (MWM) [22]. This tractability result, the first of its kind in genome rearrangements, renewed the interest in gene order median problems, although most of the following work presented intractability results, even on variations of the breakpoint distance [5,9,14]. A notable exception was the Single-Cut-or-Join (SCJ) distance, introduced by Feijão and Meidanis [11], where it was shown that both the SCJ median problem and the SCJ SPP are tractable.…”

Section: Introductionmentioning

confidence: 97%

The Rooted SCJ Median with Single Gene Duplications

et al. 2018

Comparative Genomics

The median problem is a classical problem in genome rearrangements. It aims to compute a gene order that minimizes the sum of the genomic distances to k ≥ 3 given gene orders. This problem is intractable except in the related Single-Cut-or-Join and breakpoint rearrangement models. Here we consider the rooted median problem, where we assume one of the given genomes to be ancestral to the median, which is itself ancestral to the other genomes. We show that in the Single-Cutor-Join model with single gene duplications, the rooted median problem is NP-hard. We also describe an Integer Linear Program for solving this problem, which we apply to simulated data, showing high accuracy of the reconstructed medians.

“…However, in 2009, Tannier, Zheng and Sankoff proved that computing a median gene order that is allowed to contain an arbitrary mixture of linear and circular fragments is tractable in the breakpoint distance model, by using a reduction to a Maximum Weight Matching (MWM) problem [8]. This tractability result, the first of its kind in genome rearrangement algorithms, renewed the interest in gene order median problems, although most of the following work presented intractability results, even on variations of the breakpoint distance [9,10,11]. A notable exception was the Single-Cut-or-Join (SCJ) distance, introduced by Feijão and Meidanis [12], where it was shown that both the median problem and the SPP are tractable.…”

Section: Introductionmentioning

confidence: 99%

The Distance and Median Problems in the Single-Cut-or-Join model with Single-Gene Duplications

et al. 2020

Preprint

Background: In the field of genome rearrangement algorithms, models accounting for gene duplication lead often to hard problems. For example, while computing the pairwise distance is tractable in most duplication-free models, it is NP-complete for most extensions of these models accounting for duplicated genes. Moreover, problems involving more than two genomes, such as the genome median and the Small Parsimony problem, are intractable for most duplication-free models, with some exceptions, for example the Single-Cut-or-Join (SCJ) model. Result: We introduce a variant of the SCJ distance that accounts for duplicated genes, in the context of directed evolution from an ancestral genome to a descendant genome where orthology relations between ancestral genes and their descendant are known. Our model includes two duplication mechanisms: single-gene tandem duplication and the creation of single-gene circular chromosomes. We prove that in this model, computing the directed distance and a parsimonious evolutionary scenario in terms of SCJ and single-gene duplication events can be done in linear time. We also show that the directed median problem is tractable for this distance, while the rooted median problem, where we assume that one of the given genomes is ancestral to the median, is NP-complete. We also describe an Integer Linear Program for solving this problem. We evaluate the directed distance and rooted median algorithms on simulated data. Conclusion: Our results provide a simple genome rearrangement model, extending the SCJ model to account for single-gene duplications, for which we prove a mix of tractability and hardness results. For the NP-complete rooted median problem, we design a simple Integer Linear Program. Our publicly available implementation of these algorithms for the directed distance and median problems allow to solve efficiently these problems on large instances. Availability: https://github.com/cchauve/SCJ-with-SGD