### Abstract

In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph with n vertices where each edge is colored with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e. minimum number of vertices) which has precisely one edge from each color class. In this paper we show a randomized max(√2n,√δ(1+√lnδ/2))-approximation algorithm using LP rounding, where δ is the maximum degree in the input graph. On the other hand we prove that there exists a constant c such that the minimum rainbow subgraph problem does not have a clnδ-approximation, unless NP⊆DTIME(n^{O(loglogn)}).

Original language | English |
---|---|

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Theoretical Computer Science |

Volume | 543 |

Issue number | C |

DOIs | |

Publication status | Published - 2014 |

Externally published | Yes |

### Fingerprint

### Keywords

- Approximation algorithms
- Combinatorial problems
- Minimum rainbow subgraph

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

**Better lower and upper bounds for the minimum rainbow subgraph problem.** / Popa, Alexandru.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 543, no. C, pp. 1-8. https://doi.org/10.1016/j.tcs.2014.05.008

}

TY - JOUR

T1 - Better lower and upper bounds for the minimum rainbow subgraph problem

AU - Popa, Alexandru

PY - 2014

Y1 - 2014

N2 - In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph with n vertices where each edge is colored with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e. minimum number of vertices) which has precisely one edge from each color class. In this paper we show a randomized max(√2n,√δ(1+√lnδ/2))-approximation algorithm using LP rounding, where δ is the maximum degree in the input graph. On the other hand we prove that there exists a constant c such that the minimum rainbow subgraph problem does not have a clnδ-approximation, unless NP⊆DTIME(nO(loglogn)).

AB - In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph with n vertices where each edge is colored with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e. minimum number of vertices) which has precisely one edge from each color class. In this paper we show a randomized max(√2n,√δ(1+√lnδ/2))-approximation algorithm using LP rounding, where δ is the maximum degree in the input graph. On the other hand we prove that there exists a constant c such that the minimum rainbow subgraph problem does not have a clnδ-approximation, unless NP⊆DTIME(nO(loglogn)).

KW - Approximation algorithms

KW - Combinatorial problems

KW - Minimum rainbow subgraph

UR - http://www.scopus.com/inward/record.url?scp=84909600118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84909600118&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2014.05.008

DO - 10.1016/j.tcs.2014.05.008

M3 - Article

VL - 543

SP - 1

EP - 8

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - C

ER -