An Approximation Algorithm for the Multicast Congestion Problem via Minimum Steiner Trees

We are given a graph G = (V;E) to represent a communication network where jV j = n and jEj = m and a set of multicast requests S1, : : : , Sk V . A solution is a set of k trees T1, : : : , Tk where Ti connects the vertices of Si. The goal of the multicast congestion problem is to find a solution of k trees minimizing the maximum number of times an edge is used. In this paper we present an approximation algorithm for the multicast congestion problem based on the algorithms in [15] and [2]. We show that our algorithm is able to overcome the difficulties of an exponential number of variables and a weak block solver for the Steiner tree problem. For any given error tolerance ε 2 (0;1℄ the asymptotic approximation algorithm delivers a solution with a constant ratio in O(m(lnm+ ε 2 lnε)(kβ+m ln ln(m=ε))) time, where β is the running time of the approximate solver.