### Abstract

In this paper we define a new similarity measure, the non-breaking similarity, which is the complement of the famous breakpoint distance between genomes (in general, between any two sequences drawn from the same alphabet). When the two input genomes G and ℋ, drawn from the same set of n gene families, contain gene repetitions, we consider the corresponding Exemplar Non-breaking Similarity problem (ENbS) in which we need to delete repeated genes in G and ℋ such that the resulting genomes G and H have the maximum non-breaking similarity. We have the following results. - For the Exemplar Non-breaking Similarity problem, we prove that the Independent Set problem can be linearly reduced to this problem. Hence, ENbS does not admit any factor-n^{1-ε} polynomial-time approximation unless P=NP. (Also, ENbS is W[1]-complete.) - We show that for several practically interesting cases of the Exemplar Non-breaking Similarity problem, there are polynomial time algorithms.

Original language | English (US) |
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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) |

Pages | 119-130 |

Number of pages | 12 |

Volume | 4580 LNCS |

State | Published - 2007 |

Event | 18th Annual Symposium on Combinatorial Pattern Matching, CPM 2007 - London, ON, Canada Duration: Jul 9 2007 → Jul 11 2007 |

### Publication series

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

Volume | 4580 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 18th Annual Symposium on Combinatorial Pattern Matching, CPM 2007 |
---|---|

Country | Canada |

City | London, ON |

Period | 7/9/07 → 7/11/07 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4580 LNCS, pp. 119-130). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4580 LNCS).

**Non-breaking similarity of genomes with gene repetitions.** / Chen, Zhixiang; Fu, Bin; Xu, Jinhui; Yang, Boting; Zhao, Zhiyu; Zhu, Binhai.

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. 4580 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4580 LNCS, pp. 119-130, 18th Annual Symposium on Combinatorial Pattern Matching, CPM 2007, London, ON, Canada, 7/9/07.

}

TY - GEN

T1 - Non-breaking similarity of genomes with gene repetitions

AU - Chen, Zhixiang

AU - Fu, Bin

AU - Xu, Jinhui

AU - Yang, Boting

AU - Zhao, Zhiyu

AU - Zhu, Binhai

PY - 2007

Y1 - 2007

N2 - In this paper we define a new similarity measure, the non-breaking similarity, which is the complement of the famous breakpoint distance between genomes (in general, between any two sequences drawn from the same alphabet). When the two input genomes G and ℋ, drawn from the same set of n gene families, contain gene repetitions, we consider the corresponding Exemplar Non-breaking Similarity problem (ENbS) in which we need to delete repeated genes in G and ℋ such that the resulting genomes G and H have the maximum non-breaking similarity. We have the following results. - For the Exemplar Non-breaking Similarity problem, we prove that the Independent Set problem can be linearly reduced to this problem. Hence, ENbS does not admit any factor-n1-ε polynomial-time approximation unless P=NP. (Also, ENbS is W[1]-complete.) - We show that for several practically interesting cases of the Exemplar Non-breaking Similarity problem, there are polynomial time algorithms.

AB - In this paper we define a new similarity measure, the non-breaking similarity, which is the complement of the famous breakpoint distance between genomes (in general, between any two sequences drawn from the same alphabet). When the two input genomes G and ℋ, drawn from the same set of n gene families, contain gene repetitions, we consider the corresponding Exemplar Non-breaking Similarity problem (ENbS) in which we need to delete repeated genes in G and ℋ such that the resulting genomes G and H have the maximum non-breaking similarity. We have the following results. - For the Exemplar Non-breaking Similarity problem, we prove that the Independent Set problem can be linearly reduced to this problem. Hence, ENbS does not admit any factor-n1-ε polynomial-time approximation unless P=NP. (Also, ENbS is W[1]-complete.) - We show that for several practically interesting cases of the Exemplar Non-breaking Similarity problem, there are polynomial time algorithms.

UR - http://www.scopus.com/inward/record.url?scp=37749034336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37749034336&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:37749034336

SN - 9783540734369

VL - 4580 LNCS

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

SP - 119

EP - 130

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

ER -