A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study

Bader, David A.; Moret, Bernard M. E.; Yan, Mi

doi:10.1007/3-540-44634-6_34

Cited by 96 publications

(137 citation statements)

References 20 publications

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“…Therefore, the reversal distance between A and B is one. If the direction of the genes is known and used for the computation, this is called “signed” (because the numbers in the permutations are labeled with a minus sign if the genes are found on the complement strand of the DNA) and can be computed in linear time [37,38]. If the direction of the gene is not known, it is called “unsigned.” In this case, the problem of finding the optimal sequence of reversals is NP-hard [39].…”

Section: Methodsmentioning

confidence: 99%

A Phylogenomic Study of Human, Dog, and Mouse

2007

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In recent years the phylogenetic relationship of mammalian orders has been addressed in a number of molecular studies. These analyses have frequently yielded inconsistent results with respect to some basal ordinal relationships. For example, the relative placement of primates, rodents, and carnivores has differed in various studies. Here, we attempt to resolve this phylogenetic problem by using data from completely sequenced nuclear genomes to base the analyses on the largest possible amount of data. To minimize the risk of reconstruction artifacts, the trees were reconstructed under different criteria—distance, parsimony, and likelihood. For the distance trees, distance metrics that measure independent phenomena (amino acid replacement, synonymous substitution, and gene reordering) were used, as it is highly improbable that all of the trees would be affected the same way by any reconstruction artifact. In contradiction to the currently favored classification, our results based on full-genome analysis of the phylogenetic relationship between human, dog, and mouse yielded overwhelming support for a primate–carnivore clade with the exclusion of rodents.

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Section: Methodsmentioning

confidence: 99%

A Phylogenomic Study of Human, Dog, and Mouse

2007

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“…Call this circle graph G C ; a maximum independent set of G C corresponds to a maximum independent set of commuting inversions. The HP-graph can be built in linear time [19] and a maximum independent set of G C can be computed in O ( n 2 ) time with the algorithm of Valiente [20]; we thus have the following theorem.…”

Section: Methodsmentioning

confidence: 99%

Maximum independent sets of commuting and noninterfering inversions

Swenson

Tang

et al. 2009

BMC Bioinformatics

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BackgroundGiven three signed permutations, an inversion median is a fourth permutation that minimizes the sum of the pairwise inversion distances between it and the three others. This problem is NP-hard as well as hard to approximate. Yet median-based approaches to phylogenetic reconstruction have been shown to be among the most accurate, especially in the presence of long branches. Most existing approaches have used heuristics that attempt to find a longest sequence of inversions from one of the three permutations that, at each step in the sequence, moves closer to the other two permutations; yet very little is known about the quality of solutions returned by such approaches.ResultsRecently, Arndt and Tang took a step towards finding longer such sequences by using sets of commuting inversions. In this paper, we formalize the problem of finding such sequences of inversions with what we call signatures and provide algorithms to find maximum cardinality sets of commuting and noninterfering inversions.ConclusionOur results offer a framework in which to study the inversion median problem, faster algorithms to obtain good medians, and an approach to study characteristic events along an evolutionary path.

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“…It is important to stress here that the GA maintains just a single population and that the calculation of the fitness is made by the slave processes using the linear time algorithm for sorting signed permutations in [5].…”

Section: Ga With Parallel Calculation Of the Fitness Functionmentioning

confidence: 99%

“…The value of the fitness is the optimal number of reversals for sorting the signed permutation that represents each individual, which is linearly computed through the implementation of the exact algorithm proposed, and provided in [5].…”

Section: Background and Standard Ga For Suprmentioning

confidence: 99%

“…After that, more efficient algorithms based on the exact polynomial algorithms in [14] have been introduced; among them, the O(nα(n)) time algorithm proposed in [7], where α(n) is the inverse of Ackermann's function and, the linear time algorithm proposed in [5] that uses a new data structure called overlap forest. These algorithms can be applied, increasing their complexities, not only to compute the reversal distance, but also to build a minimal sequence of sorting reversals.…”

Section: Introductionmentioning

confidence: 99%

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Parallelization of genetic algorithms for sorting permutations by reversals over biological data

Soncco-Álvarez

Almeida

Becker

et al. 2015

HIS

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Reversals are operations of great biological significance for the analysis of the evolutionary distance between organisms. Genome rearrangement through reversals, consists in finding the shortest sequence of reversals to transform one genome represented as a signed or unsigned permutation into another. When genes are non oriented and correspondingly permutations are unsigned, sorting by reversals came arise as a challenging problem in combinatorics of permutations. In fact, this problem is known to be N P-hard, but the question whether it is N P-complete remains open for more than twenty years. When permutations are signed and correspondingly genes are oriented, the problem is known to be in P. A parallelization of a standard GA (Genetic Algorithm) is proposed for the problem of sorting unsigned permutations. This GA was previously reported in the literature as the most competitive regarding precision for which as control mechanism an 1.5-approximation algorithm was used. For the parallelization, the MPI Library of the C language was used and experiments were performed for calculating the execution time and precision. By increasing the number of individuals, experiment showed improvement in relation to previous approaches. Additionally, a virtualization of the GA using a MicroBlaze processor from Xilinx was performed on OVP for which the average number of executed instructions was of approximately 1.40 Giga instruction per second. In this extended version of this works originally presented in NaBIC 2013 biological data was generated and it was shown how the parallelization can be applied for their analysis. Specifically, the evolutionary distances between different pairs of organism were computed based on the set of non common genes in their mitochondrial DNA genome and the reversal distance between the sequences of common genes.

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A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study

Cited by 96 publications

References 20 publications

A Phylogenomic Study of Human, Dog, and Mouse

A Phylogenomic Study of Human, Dog, and Mouse

Maximum independent sets of commuting and noninterfering inversions

Parallelization of genetic algorithms for sorting permutations by reversals over biological data

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