## Abstract

This paper presents approximation algorithms for two extensions of the set cover problem: a graph-based extension known as the Max-Rep or Label-Cover_{MAX}problem, and a color-based extension known as the Red-Blue Set Cover problem. First, a randomized algorithm guaranteeing approximation ratio sqrt(n) with high probability is proposed for the Max-Rep (or Label-Cover_{MAX}) problem, where n is the number of vertices in the graph. This algorithm is then generalized into a 4 sqrt(n)-ratio algorithm for the nonuniform version of the problem. Secondly, it is shown that the Red-Blue Set Cover problem can be approximated with ratio 2 sqrt(n log β), where n is the number of sets and β is the number of blue elements. Both algorithms can be adapted to the weighted variants of the respective problems, yielding the same approximation ratios.

Original language | English |
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Pages (from-to) | 55-64 |

Number of pages | 10 |

Journal | Journal of Discrete Algorithms |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2007 |

Externally published | Yes |

## Keywords

- Approximation algorithms
- Label Cover
- Max-Rep problem
- Red-Blue Set Cover

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