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.Comment: Conference version in WADS'9