## Abstract

We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and to the covering problem that are within a factor of 2 of each other. Each of these results implies an approximative min-max result. For the general case of arbitrary weights and capacities we describe an LP-based (2 + epsilon)-approximation algorithm for the covering problem. Finally, we show that, unless P = NP, the covering problem cannot be approximated in polynomial time within arbitrarily good precision.

Original language | English |
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Pages (from-to) | 53-71 |

Number of pages | 19 |

Journal | Rairo-Operations research |

Volume | 36 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 |

## Keywords

- primal-dual
- approximation algorithms
- packing-covering
- intervals
- THROUGHPUT