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ICALP

2003

Springer

2003

Springer

We consider requests for capacity in a given tree network T = (V, E) where each edge of the tree has some integer capacity ue. Each request consists of an integer demand df and a proﬁt wf which is obtained if the request is satisﬁed. The objective is to ﬁnd a set of demands that can be feasibly routed in the tree and which provide a maximum proﬁt. This generalizes well-known problems including the knapsack and b-matching problems. When all demands are 1, we have the integer multicommodity ﬂow problem. Garg, Vazirani, and Yannakakis had shown that this problem is NP-hard and gave a 2-approximation algorithm for the cardinality case (all proﬁts are 1) via a primal-dual algorithm. Our main result establishes that the natural linear programming relaxation has a constant factor gap, a factor of 4. Our proof is based on colouring paths on trees and this has other applications for wavelength assignment in optical network routing. We then consider the problem with arbitrary demand...

Related Content

Added |
06 Jul 2010 |

Updated |
06 Jul 2010 |

Type |
Conference |

Year |
2003 |

Where |
ICALP |

Authors |
Chandra Chekuri, Marcelo Mydlarz, F. Bruce Shepherd |

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