Designing Multi-Commodity Flow Trees
<|reference_start|>Designing Multi-Commodity Flow Trees: 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). This improves the O(log^2 n) approximation factor that is trivial to obtain by a direct application of the balanced-separator method.<|reference_end|>
@article{khuller2002designing,
    title={Designing Multi-Commodity Flow Trees},
    author={Samir Khuller, Balaji Raghavachari, Neal E. Young},
    journal={Information Processing Letters 50:49-55 (1994)},
    year={2002},
    doi={10.1016/0020-0190(94)90044-2},
    archivePrefix={arXiv},
    eprint={cs/0205077},
    primaryClass={cs.DS cs.DM}
}