## Abstract

A set V and a collection of (possibly nondisjoint) subsets are given. Also given is a real matrix describing distances between elements of V. A cover is a subset of V containing at least one representative from each subset. The multiple-choice minimum-diameter problem is to select a cover of minimum diameter. The diameter is defined as the maximum distance between any pair of elements in the cover. The multiple-choice dispersion problem, which is closely related, asks us to maximize the minimum distance between any pair of elements in the cover. The problems are NP-hard. We present polynomial time algorithms for approximating special cases and generalizations of these basic problems, and we prove in other cases that no such algorithms exist (assuming P ≉ NP).

Original language | English |
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Pages (from-to) | 147-155 |

Number of pages | 9 |

Journal | Networks |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - Oct 2000 |

## Keywords

- Approximation algorithms
- Covering problems
- Graph diameter
- NP-complete