Multicommodity Demand Flow in a Tree

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...

• Type: Conference
• Year: 2003
• Where: ICALP
• Authors: Chandra Chekuri, Marcelo Mydlarz, F. Bruce Shepherd
• Keywords: ICALP 2003, Integer Capacity Ue, Integer Demand Df, Integrality Gap, Theoretical Computer Science