## Samenvatting

The School Bus Problem is an NP-hard vehicle routing problem in which the goal is to route buses that transport children to a school such that for each child, the distance travelled on the bus does not exceed the shortest distance from the child's home to the school by more than a given regret threshold. Subject to this constraint and bus capacity limit, the goal is to minimize the number of buses required. In this paper, we give a polynomial time 4-approximation algorithm when the children and school are located at vertices of a fixed tree. As a byproduct of our analysis, we show that the integrality gap of the natural set-cover formulation for this problem is also bounded by 4. We also present a constant factor approximation for the variant where we have a fixed number of buses to use, and the goal is to minimize the maximum regret.

Originele taal-2 | Engels |
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Pagina's (van-tot) | 49-64 |

Aantal pagina's | 16 |

Tijdschrift | Algorithmica |

Volume | 67 |

Nummer van het tijdschrift | 1 |

DOI's | |

Status | Gepubliceerd - 1 jan. 2013 |

Extern gepubliceerd | Ja |