Designing Multi - Commodity Flow
نویسندگان
چکیده
The traditional multi-commodity ow problem assumes a given ow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity ow network-design problem: given a set of multi-commodity ow demands, nd 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.
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