DESIGNING MULTICOMMODITY FLOW TREES

The traditional multi-commodity flow problem assumes a given flow netw ork in which multiple commodities are to be maximally routed in respon se to given demands. This paper considers the multi-commodity flow net work-design problem: given a set of multi-commodity flow demands, find a network subject to certain constraints such that the commodities ca n be maximally routed. This paper focuses on the case when the network is required to be a tree. The main result is an approximation algorit hm for the case when the tree is required to be of constant degree. Th e algorithm reduces the problem to the minimum-weight balanced-separat or problem; the performance guarantee of the algorithm is within a fac tor of 4 of the performance guarantee of the balanced-separator proced ure. If Leighton and Rao's balanced-separator procedure is used, the p erformance guarantee is O(log n). This improves the O(log(2)n) approxi mation factor obtained by a direct application of the balanced-separat or method.