## Abstract

The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-design problem: given a set of multi-commodity flow demands, find a network subject to certain constraints such that the commodities can be maximally routed. This paper focuses on the case when the network is required to be a tree. The main result is an approximation algorithm for the case when the tree is required to be of constant degree. The algorithm reduces the problem to the minimum-weight balanced-separator problem; the performance guarantee of the algorithm is within a factor of 4 of the performance guarantee of the balanced-separator procedure. If Leighton and Rao's balanced-separator procedure is used, the performance guarantee is O(log n).

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

Title of host publication | Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings |

Editors | Frank Dehne, Jorg-Rudiger Sack, Nicola Santoro, Sue Whitesides |

Publisher | Springer Verlag |

Pages | 433-441 |

Number of pages | 9 |

ISBN (Print) | 9783540571551 |

DOIs | |

State | Published - 1993 |

Event | 3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada Duration: Aug 11 1993 → Aug 13 1993 |

### Publication series

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

Volume | 709 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Workshop on Algorithms and Data Structures, WADS 1993 |
---|---|

Country/Territory | Canada |

City | Montreal |

Period | 8/11/93 → 8/13/93 |

### Funding

We consider the case when the network is required to be a tree, called the tree congestion problem. Given a tree in which the vertices of G are embedded, the load on an edge e is defined as follows: delete e from T. This breaks T into two connected "Department of Computer Science, University of Maryland, College Park, MD 20742. E-mail : s amir@r umd. edu. tComputer Science Department, Pennsylvania State University, University Park, PA 16802. E-mail : :rbkQcs. psu. edu. Part of this work was done while this author was visiting UMIACS. lInstitute for Advanced Computer Studies, University of Maryland, College Park, MD 20742. E-mail : you.ugCm~iacs.umd.eda. Research supported in part by NSF grants CCR-8906949 and CCK-9111348.

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science