### Abstract

The evolutionary distance between two organisms can be determined by comparing the order of appearance of orthologous genes in their genomes. Above the numerous parsimony approaches that try to obtain the shortest sequence of rearrangement operations sorting one genome into the other, Bayesian Markov chain Monte Carlo methods have been introduced a few years ago. The computational time for convergence in the Markov chain is the product of the number of needed steps in the Markov chain and the computational time needed to perform one MCMC step. Therefore faster methods for making one MCMC step can reduce the mixing time of an MCMC in terms of computer running time. We introduce two efficient algorithms for characterizing and sampling transpositions and inverted transpositions for Bayesian MCMC. The first algorithm characterizes the transpositions and inverted transpositions by the number of breakpoints the mutations change in the breakpoint graph, the second algorithm characterizes the mutations by the change in the number of cycles. Both algorithms run in O(n) time, where n is the size of the genome. This is a significant improvement compared with the so far available brute force method with O(n^{3}) running time and memory usage.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 174-185 |

Number of pages | 12 |

Volume | 4175 LNBI |

ISBN (Print) | 3540395830, 9783540395836 |

Publication status | Published - 2006 |

Event | 6th International Workshop on Algorithms in Bioinformatics, WABI 2006 - Zurich, Switzerland Duration: Sep 11 2006 → Sep 13 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4175 LNBI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th International Workshop on Algorithms in Bioinformatics, WABI 2006 |
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Country | Switzerland |

City | Zurich |

Period | 9/11/06 → 9/13/06 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4175 LNBI, pp. 174-185). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4175 LNBI). Springer Verlag.

**Efficient sampling of transpositions and inverted transpositions for Bayesian MCMC.** / Miklós, I.; Paige, Timothy Brooks; Ligeti, Péter.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 4175 LNBI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4175 LNBI, Springer Verlag, pp. 174-185, 6th International Workshop on Algorithms in Bioinformatics, WABI 2006, Zurich, Switzerland, 9/11/06.

}

TY - GEN

T1 - Efficient sampling of transpositions and inverted transpositions for Bayesian MCMC

AU - Miklós, I.

AU - Paige, Timothy Brooks

AU - Ligeti, Péter

PY - 2006

Y1 - 2006

N2 - The evolutionary distance between two organisms can be determined by comparing the order of appearance of orthologous genes in their genomes. Above the numerous parsimony approaches that try to obtain the shortest sequence of rearrangement operations sorting one genome into the other, Bayesian Markov chain Monte Carlo methods have been introduced a few years ago. The computational time for convergence in the Markov chain is the product of the number of needed steps in the Markov chain and the computational time needed to perform one MCMC step. Therefore faster methods for making one MCMC step can reduce the mixing time of an MCMC in terms of computer running time. We introduce two efficient algorithms for characterizing and sampling transpositions and inverted transpositions for Bayesian MCMC. The first algorithm characterizes the transpositions and inverted transpositions by the number of breakpoints the mutations change in the breakpoint graph, the second algorithm characterizes the mutations by the change in the number of cycles. Both algorithms run in O(n) time, where n is the size of the genome. This is a significant improvement compared with the so far available brute force method with O(n3) running time and memory usage.

AB - The evolutionary distance between two organisms can be determined by comparing the order of appearance of orthologous genes in their genomes. Above the numerous parsimony approaches that try to obtain the shortest sequence of rearrangement operations sorting one genome into the other, Bayesian Markov chain Monte Carlo methods have been introduced a few years ago. The computational time for convergence in the Markov chain is the product of the number of needed steps in the Markov chain and the computational time needed to perform one MCMC step. Therefore faster methods for making one MCMC step can reduce the mixing time of an MCMC in terms of computer running time. We introduce two efficient algorithms for characterizing and sampling transpositions and inverted transpositions for Bayesian MCMC. The first algorithm characterizes the transpositions and inverted transpositions by the number of breakpoints the mutations change in the breakpoint graph, the second algorithm characterizes the mutations by the change in the number of cycles. Both algorithms run in O(n) time, where n is the size of the genome. This is a significant improvement compared with the so far available brute force method with O(n3) running time and memory usage.

UR - http://www.scopus.com/inward/record.url?scp=33750278904&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750278904&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540395830

SN - 9783540395836

VL - 4175 LNBI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 174

EP - 185

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -