Sorting Circular Permutations by Super Short Reversals

Galvão, Gustavo Rodrigues; Baudet, Christian; Dias, Zanoni

doi:10.1109/tcbb.2016.2515594

Cited by 12 publications

(8 citation statements)

References 22 publications

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“…In 2016, Galvão et al [ 14 ] proved that Sorting Signed Permutations by cyclic super short reversals is also in . Given a signed permutation and a VD-vector X , let be the set of elements from such that is even and , and let be the set of elements from such that is odd and .…”

Section: Related Resultsmentioning

confidence: 99%

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Sorting signed circular permutations by super short operations

Oliveira

Fertin

Dias

et al. 2018

Algorithms Mol Biol

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BackgroundOne way to estimate the evolutionary distance between two given genomes is to determine the minimum number of large-scale mutations, or genome rearrangements, that are necessary to transform one into the other. In this context, genomes can be represented as ordered sequences of genes, each gene being represented by a signed integer. If no gene is repeated, genomes are thus modeled as signed permutations of the form , and in that case we can consider without loss of generality that one of them is the identity permutation , and that we just need to sort the other (i.e., transform it into ). The most studied genome rearrangement events are reversals, where a segment of the genome is reversed and reincorporated at the same location; and transpositions, where two consecutive segments are exchanged. Many variants, e.g., combining different types of (possibly constrained) rearrangements, have been proposed in the literature. One of them considers that the number of genes involved, in a reversal or a transposition, is never greater than two, which is known as the problem of sorting by super short operations (or SSOs).Results and conclusionsAll problems considering SSOs in permutations have been shown to be in , except for one, namely sorting signed circular permutations by super short reversals and super short transpositions. Here we fill this gap by introducing a new graph structure called cyclic permutation graph and providing a series of intermediate results, which allows us to design a polynomial algorithm for sorting signed circular permutations by super short reversals and super short transpositions.

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Section: Related Resultsmentioning

confidence: 99%

“…The following property was given by Jerrum [ 13 ]. Note that the author mistakenly wrote , which was later corrected by Galvão et al [ 14 ].…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Sorting signed circular permutations by super short operations

Oliveira

Fertin

Dias

et al. 2018

Algorithms Mol Biol

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“…Aside from problems that consider rearrangement length, little is known about weighted rearrangements [ 16 – 20 ]. In [ 9 ], we showed that with a simple cost function based on a partition of the adjacencies of one of the genomes into equivalence classes, one can choose—from the exponentially large set of shortest scenarios—a scenario that minimizes the number of moves acting across classes.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Finding local genome rearrangements

Simonaitis

Swenson

2018

Algorithms Mol Biol

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BackgroundThe double cut and join (DCJ) model of genome rearrangement is well studied due to its mathematical simplicity and power to account for the many events that transform gene order. These studies have mostly been devoted to the understanding of minimum length scenarios transforming one genome into another. In this paper we search instead for rearrangement scenarios that minimize the number of rearrangements whose breakpoints are unlikely due to some biological criteria. One such criterion has recently become accessible due to the advent of the Hi-C experiment, facilitating the study of 3D spacial distance between breakpoint regions.ResultsWe establish a link between the minimum number of unlikely rearrangements required by a scenario and the problem of finding a maximum edge-disjoint cycle packing on a certain transformed version of the adjacency graph. This link leads to a 3/2-approximation as well as an exact integer linear programming formulation for our problem, which we prove to be NP-complete. We also present experimental results on fruit flies, showing that Hi-C data is informative when used as a criterion for rearrangements.ConclusionsA new variant of the weighted DCJ distance problem is addressed that ignores scenario length in its objective function. A solution to this problem provides a lower bound on the number of unlikely moves necessary when transforming one gene order into another. This lower bound aids in the study of rearrangement scenarios with respect to chromatin structure, and could eventually be used in the design of a fixed parameter algorithm with a more general objective function.

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“…Recently, the full version of the conference paper corresponding to Chapter 6 has been accepted for publication in IEEE/ACM Transactions on Computational Biology and Bioinformatics [Galvão et al 2016]. The first relevant difference between the journal version and the conference version of the paper is that the journal version contains expanded explanations and expositions of the methods.…”

Section: Contributions and Organizationmentioning

confidence: 99%

Algorithms for Sorting by Reversals or Transpositions, with Application to Genome Rearrangement

Galvão¹,

Dias²

2016

Anais Do XXIX Concurso De Teses E Dissertações (CTD 2016)

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The problem of finding the minimum sequence of rearrangements that transforms one genome into another is a well-studied problem that finds application in comparative genomics. Representing genomes as permutations, in which genes appear as elements, that problem can be reduced to the combinatorial problem of sorting a permutation using a minimum number of rearrangements. Such combinatorial problem varies according to the types of rearrangements considered. The PhD thesis summarized in this paper presents exact, approximation, and heuristic algorithms for solving variants of the permutation sorting problem involving two types of rearrangements: reversals and transpositions.

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Sorting Circular Permutations by Super Short Reversals

Cited by 12 publications

References 22 publications

Sorting signed circular permutations by super short operations

Sorting signed circular permutations by super short operations

Finding local genome rearrangements

Algorithms for Sorting by Reversals or Transpositions, with Application to Genome Rearrangement

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