## Finding an optimal inversion median: experimental results (2001)

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Venue: | In Proc. 1st Workshop on Algs. in Bioinformatics WABI 2001 |

Citations: | 25 - 10 self |

### BibTeX

@INPROCEEDINGS{Siepel01findingan,

author = {Adam C. Siepel and Bernard M. E. Moret},

title = {Finding an optimal inversion median: experimental results},

booktitle = {In Proc. 1st Workshop on Algs. in Bioinformatics WABI 2001},

year = {2001},

pages = {189--203},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

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### Abstract

Abstract. We derive a branch-and-bound algorithm to find an optimal inversion median of three signed permutations. The algorithm prunes to manageable size an extremely large search tree using simple geometric properties of the problem and a newly available linear-time routine for inversion distance. Our experiments on simulated data sets indicate that the algorithm finds optimal medians in reasonable time for genomes of medium size when distances are not too large, as commonly occurs in phylogeny reconstruction. In addition, we have compared inversion and breakpoint medians, and found that inversion medians generally score significantly better and tend to be far more unique, which should make them valuable in median-based tree-building algorithms. 1

### Citations

270 | Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
- Hannenhalli, Pevzner
- 1999
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Citation Context ... sorting by inversions (or reversals, as they are often called in computer science) has produced a duality theorem and polynomial-time algorithm for inversion distance between two signed permutations =-=[10]-=-, a duality theorem and polynomial-time algorithm for distance in terms of equally weighted translocations and inversions for signed permutations [11], polynomial-time algorithms for sorting by revers... |

209 |
Introduction to Computational Molecular Biology
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Citation Context ... of rearrangement-based techniques for phylogenetic purposes and initiated what is now nearly a decade of intense interest in computational problems relating to genome rearrangement (see summaries in =-=[16, 19, 22]-=-). While much of the attention given to rearrangement problems may be due to their intriguing combinatorial properties, rearrangement-based approaches to phylogenetic inference are of genuine biologic... |

162 |
Computational Molecular Biology: An Algorithmic Approach
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- 2000
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Citation Context ... of rearrangement-based techniques for phylogenetic purposes and initiated what is now nearly a decade of intense interest in computational problems relating to genome rearrangement (see summaries in =-=[16, 19, 22]-=-). While much of the attention given to rearrangement problems may be due to their intriguing combinatorial properties, rearrangement-based approaches to phylogenetic inference are of genuine biologic... |

110 | A linear-time algorithm for computing inversion distance between signed permutations with an experimental study
- Bader, Moret, et al.
(Show Context)
Citation Context ...equally weighted translocations and inversions for signed permutations [11], polynomial-time algorithms for sorting by reversals [2, 12], and a linear-time algorithm for computing inversion distances =-=[1]. Note tha-=-t "signed permutations" correspond to genomes for which the direction of transcription of each gene is known as well as the ordering of the genes. Much recent work on rearrangement-based phy... |

106 | A faster and simpler algorithm for sorting signed permutations by reversals
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- 1999
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Citation Context ...duality theorem and polynomial-time algorithm for distance in terms of equally weighted translocations and inversions for signed permutations [11], polynomial-time algorithms for sorting by reversals =-=[2, 12], and a li-=-near-time algorithm for computing inversion distances [1]. Note that "signed permutations" correspond to genomes for which the direction of transcription of each gene is known as well as the... |

81 | Transforming men into mice (polynomial algorithm for genomic distance problems
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Citation Context ...nversion distance between two signed permutations [10], a duality theorem and polynomial-time algorithm for distance in terms of equally weighted translocations and inversions for signed permutations =-=[11], polynomi-=-al-time algorithms for sorting by reversals [2, 12], and a linear-time algorithm for computing inversion distances [1]. Note that "signed permutations" correspond to genomes for which the di... |

78 |
Gene order comparisons for phylogenetic inference: Evolution of the mitochondrial genome
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Citation Context ... Watterson et al. [23] first proposed the minimum number of chromosomal inversions necessary to transform one ordering into another as an appropriate distance metric. The 1992 study by Sankoff et al. =-=[21]-=- included a heuristic algorithm for finding rearrangement distance (which considered transpositions, insertions, and deletions, as well as inversions); it was the first large-scale application and exp... |

77 | Multiple genome rearrangement and breakpoint phylogeny
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Citation Context ...oaches perform poorly, such as when species diverged early or are rapidly evolving [16]. In addition, rearrangement-based phylogenetic methods can suggest probable gene orderings of ancestral species =-=[17, 18]-=-, while other methods cannot. Furthermore, mathematical models of genome rearrangement have applications beyond phylogeny (see [8, 20]). Recent work on rearrangement distance and sorting by inversions... |

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- 2001
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Citation Context ...that "signed permutations" correspond to genomes for which the direction of transcription of each gene is known as well as the ordering of the genes. Much recent work on rearrangement-based =-=phylogeny [5, 6, 14, 15, 18]-=- stems from an algorithm by Sankoff and Blanchette [17] that iterates over a prospective tree, repeatedly finds medians of the three permutations adjacent to each internal vertex, and uses them to imp... |

51 | An empirical comparison of phylogenetic methods on chloroplast gene order data in Campanulaceae
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- 2000
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Citation Context ...that "signed permutations" correspond to genomes for which the direction of transcription of each gene is known as well as the ordering of the genes. Much recent work on rearrangement-based =-=phylogeny [5, 6, 14, 15, 18]-=- stems from an algorithm by Sankoff and Blanchette [17] that iterates over a prospective tree, repeatedly finds medians of the three permutations adjacent to each internal vertex, and uses them to imp... |

50 | Fast sorting by reversal, in
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- 1996
(Show Context)
Citation Context ...duality theorem and polynomial-time algorithm for distance in terms of equally weighted translocations and inversions for signed permutations [11], polynomial-time algorithms for sorting by reversals =-=[2, 12], and a li-=-near-time algorithm for computing inversion distances [1]. Note that "signed permutations" correspond to genomes for which the direction of transcription of each gene is known as well as the... |

46 |
D: Parametric genome rearrangement
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- 1996
(Show Context)
Citation Context ... distance (an inversion can remove at most two breakpoints) but the relationship is a loose one. Because it is believed that inversions are the primary mechanism of genome rearrangement for many taxa =-=[13, 3]-=-, we seek a solution to the median problem based directly on inversion distance. Finding an inversion median is known to be NP-hard [4], and to date, no one has reported a reasonably efficient algorit... |

41 | New approaches for reconstructing phylogenies from gene order data
- Moret, Wang, et al.
- 2001
(Show Context)
Citation Context ...that "signed permutations" correspond to genomes for which the direction of transcription of each gene is known as well as the ordering of the genes. Much recent work on rearrangement-based =-=phylogeny [5, 6, 14, 15, 18]-=- stems from an algorithm by Sankoff and Blanchette [17] that iterates over a prospective tree, repeatedly finds medians of the three permutations adjacent to each internal vertex, and uses them to imp... |

37 | Genome sequence comparison and scenarios for gene rearrangements: a test case, Genomics 30
- Hannenhalli, Chappey, et al.
- 1995
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Citation Context ...ion distance. Finding an inversion median is known to be NP-hard [4], and to date, no one has reported a reasonably efficient algorithm (approximate or exact) for this problem. (Although in one study =-=[9]-=-, inversion medians were obtained for a particular data set using a bounded exhaustive search.) In this paper, we present a simple yet effective branch-and-bound algorithm to solve the median of three... |

37 |
The chromosome inversion problem
- Watterson, Ewens, et al.
- 1982
(Show Context)
Citation Context ...urtevant [7] first proposed using the degree to which gene orders differ between species as an indicator of evolutionary distance that could be useful for phylogenetic inference, and Watterson et al. =-=[23]-=- first proposed the minimum number of chromosomal inversions necessary to transform one ordering into another as an appropriate distance metric. The 1992 study by Sankoff et al. [21] included a heuris... |

29 | A New Fast Heuristic for Computing the Breakpoint Phylogeny and Experimental Phylogenetic Analyses of Real and Synthetic data
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Citation Context |

20 |
The Y chromosome of Drosophila pseudoobscura
- Dobzhansky
- 1935
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Citation Context ...version medians generally score significantly better and tend to be far more unique, which should make them valuable in median-based tree-building algorithms. 1 Introduction Dobzhansky and Sturtevant =-=[7]-=- first proposed using the degree to which gene orders differ between species as an indicator of evolutionary distance that could be useful for phylogenetic inference, and Watterson et al. [23] first p... |

18 | 2000a) Early eukaryote evolution based on mitochondrial gene order breakpoints
- Sankoff, Bryant, et al.
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Citation Context ...oaches perform poorly, such as when species diverged early or are rapidly evolving [16]. In addition, rearrangement-based phylogenetic methods can suggest probable gene orderings of ancestral species =-=[17, 18]-=-, while other methods cannot. Furthermore, mathematical models of genome rearrangement have applications beyond phylogeny (see [8, 20]). Recent work on rearrangement distance and sorting by inversions... |

17 |
Conserved segment identification
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Citation Context ...methods can suggest probable gene orderings of ancestral species [17, 18], while other methods cannot. Furthermore, mathematical models of genome rearrangement have applications beyond phylogeny (see =-=[8, 20]-=-). Recent work on rearrangement distance and sorting by inversions (or reversals, as they are often called in computer science) has produced a duality theorem and polynomial-time algorithm for inversi... |

14 |
Formulations and complexity of multiple sorting by reversals, manuscript
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- 1998
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Citation Context ... the primary mechanism of genome rearrangement for many taxa [13, 3], we seek a solution to the median problem based directly on inversion distance. Finding an inversion median is known to be NP-hard =-=[4]-=-, and to date, no one has reported a reasonably efficient algorithm (approximate or exact) for this problem. (Although in one study [9], inversion medians were obtained for a particular data set using... |

10 |
High frequency of inversions during eukaryote gene order evolution
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- 2000
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Citation Context ... distance (an inversion can remove at most two breakpoints) but the relationship is a loose one. Because it is believed that inversions are the primary mechanism of genome rearrangement for many taxa =-=[13, 3]-=-, we seek a solution to the median problem based directly on inversion distance. Finding an inversion median is known to be NP-hard [4], and to date, no one has reported a reasonably efficient algorit... |

7 | Algorithms for constructing comparative maps
- Goldberg, McCouch, et al.
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Citation Context ...methods can suggest probable gene orderings of ancestral species [17, 18], while other methods cannot. Furthermore, mathematical models of genome rearrangement have applications beyond phylogeny (see =-=[8, 20]-=-). Recent work on rearrangement distance and sorting by inversions (or reversals, as they are often called in computer science) has produced a duality theorem and polynomial-time algorithm for inversi... |

1 |
Algorithms for constructing comparative maps.In
- Goldberg, McCouch, et al.
- 1995
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Citation Context ... methods can suggest probable gene orderingsof ancestral species [17, 18], while other methods cannot. Furthermore, mathematical models of genome rearrangement have applications beyond phylogeny (see =-=[8, 20]-=-).sRecent work on rearrangement distance and sorting by inversions (or reversals,as they are often called in computer science) has produced a duality theorem and polynomial-time algorithm for inversio... |