### 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 | Combinatorial Pattern Matching - 18th Annual Symposium, CPM 2007, Proceedings |

Pages | 119-130 |

Number of pages | 12 |

State | Published - Dec 1 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) |
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Volume | 4580 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

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

City | London, ON |

Period | 7/9/07 → 7/11/07 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Pattern Matching - 18th Annual Symposium, CPM 2007, Proceedings*(pp. 119-130). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4580 LNCS).