### Abstract

First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general (non-necessarily geometric) capacitated set cover problem. There is given a set of elements with real weights and a family of sets of the elements. One can use a set if it is a subset of one of the sets in the family and the sum of the weights of its elements is at most one. The goal is to cover all the elements with the allowed sets. We show that any polynomial-time algorithm that approximates the uncapacitated version of the set cover problem with ratio r can be converted to an approximation algorithm for the capacitated version with ratio r+1.357. The composition of these two results yields a polynomial-time approximation algorithm for the problem of covering a set of customers represented by a weighted n-point set with a minimum number of antennas of variable angular range and fixed capacity with ratio 2.357.

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

Title of host publication | Computing and Combinatorics - 16th Annual International Conference, COCOON 2010, Proceedings |

Pages | 226-234 |

Number of pages | 9 |

DOIs | |

Publication status | Published - Aug 3 2010 |

Event | 16th Annual International Computing and Combinatorics Conference, COCOON 2010 - Nha Trang, Viet Nam Duration: Jul 19 2010 → Jul 21 2010 |

### Publication series

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

Volume | 6196 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th Annual International Computing and Combinatorics Conference, COCOON 2010 |
---|---|

Country | Viet Nam |

City | Nha Trang |

Period | 7/19/10 → 7/21/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Computing and Combinatorics - 16th Annual International Conference, COCOON 2010, Proceedings*(pp. 226-234). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6196 LNCS). https://doi.org/10.1007/978-3-642-14031-0_26