## Abstract

We study a capacitated network design problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support the flow at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (ρ_{ST} + 2) where ρ_{ST} is the performance ratio of any approximation algorithm for the minimum Steiner tree problem. When all sources have unit demand, the ratio improves to ρ_{ST} + 1) and, in particular, to 2 when all nodes in the graph are sources.

Original language | English |
---|---|

Pages (from-to) | 417-431 |

Number of pages | 15 |

Journal | Algorithmica |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Dec 2003 |

## Keywords

- Approximation algorithms
- Capacity installation
- Network design
- Routing flow