### Abstract

In this paper, we apply a measure, exemplar adjacency number, which complements and extends the well-studied breakpoint distance between two permutations, to measure the similarity between two genomes (or in general, between any two sequences drawn from the same alphabet). For two genomes G and H drawn from the same set of n gene families and containing gene repetitions, we consider the corresponding Exemplar Adjacency Number problem (EAN), in which we delete duplicated genes from G and H such that the resultant exemplar genomes (permutations) G and H have the maximum adjacency number. We obtain the following results. First, we prove that the one-sided 2-repetitive EAN problem, i.e., when one of G and H is given exemplar and each gene occurs in the other genome at most twice, can be linearly reduced from the Maximum Independent Set problem. This implies that EAN does not admit any O(n^{0.5-ε})-approximation algorithm, for any ε>0, unless P = NP. This hardness result also implies that EAN, parameterized by the optimal solution value, is W[1]-hard. Secondly, we show that the two-sided 2-repetitive EAN problem has an O(n^{0.5})-approximation algorithm, which is tight up to a constant factor.

Original language | English (US) |
---|---|

Pages (from-to) | 59-65 |

Number of pages | 7 |

Journal | Theoretical Computer Science |

Volume | 550 |

Issue number | C |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Adjacency
- Approximation algorithm
- Breakpoint
- Genome comparison
- NP-hard

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*550*(C), 59-65. https://doi.org/10.1016/j.tcs.2014.07.011

**On the approximability of the exemplar adjacency number problem for genomes with gene repetitions.** / Chen, Zhixiang; Fu, Bin; Goebel, Randy; Lin, Guohui; Tong, Weitian; Xu, Jinhui; Yang, Boting; Zhao, Zhiyu; Zhu, Binhai.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 550, no. C, pp. 59-65. https://doi.org/10.1016/j.tcs.2014.07.011

}

TY - JOUR

T1 - On the approximability of the exemplar adjacency number problem for genomes with gene repetitions

AU - Chen, Zhixiang

AU - Fu, Bin

AU - Goebel, Randy

AU - Lin, Guohui

AU - Tong, Weitian

AU - Xu, Jinhui

AU - Yang, Boting

AU - Zhao, Zhiyu

AU - Zhu, Binhai

PY - 2014

Y1 - 2014

N2 - In this paper, we apply a measure, exemplar adjacency number, which complements and extends the well-studied breakpoint distance between two permutations, to measure the similarity between two genomes (or in general, between any two sequences drawn from the same alphabet). For two genomes G and H drawn from the same set of n gene families and containing gene repetitions, we consider the corresponding Exemplar Adjacency Number problem (EAN), in which we delete duplicated genes from G and H such that the resultant exemplar genomes (permutations) G and H have the maximum adjacency number. We obtain the following results. First, we prove that the one-sided 2-repetitive EAN problem, i.e., when one of G and H is given exemplar and each gene occurs in the other genome at most twice, can be linearly reduced from the Maximum Independent Set problem. This implies that EAN does not admit any O(n0.5-ε)-approximation algorithm, for any ε>0, unless P = NP. This hardness result also implies that EAN, parameterized by the optimal solution value, is W[1]-hard. Secondly, we show that the two-sided 2-repetitive EAN problem has an O(n0.5)-approximation algorithm, which is tight up to a constant factor.

AB - In this paper, we apply a measure, exemplar adjacency number, which complements and extends the well-studied breakpoint distance between two permutations, to measure the similarity between two genomes (or in general, between any two sequences drawn from the same alphabet). For two genomes G and H drawn from the same set of n gene families and containing gene repetitions, we consider the corresponding Exemplar Adjacency Number problem (EAN), in which we delete duplicated genes from G and H such that the resultant exemplar genomes (permutations) G and H have the maximum adjacency number. We obtain the following results. First, we prove that the one-sided 2-repetitive EAN problem, i.e., when one of G and H is given exemplar and each gene occurs in the other genome at most twice, can be linearly reduced from the Maximum Independent Set problem. This implies that EAN does not admit any O(n0.5-ε)-approximation algorithm, for any ε>0, unless P = NP. This hardness result also implies that EAN, parameterized by the optimal solution value, is W[1]-hard. Secondly, we show that the two-sided 2-repetitive EAN problem has an O(n0.5)-approximation algorithm, which is tight up to a constant factor.

KW - Adjacency

KW - Approximation algorithm

KW - Breakpoint

KW - Genome comparison

KW - NP-hard

UR - http://www.scopus.com/inward/record.url?scp=84926318071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84926318071&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2014.07.011

DO - 10.1016/j.tcs.2014.07.011

M3 - Article

AN - SCOPUS:84926318071

VL - 550

SP - 59

EP - 65

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - C

ER -