WHEN TREES COLLIDE - AN APPROXIMATION ALGORITHM FOR THE GENERALIZED STEINER PROBLEM ON NETWORKS

We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with link-costs and, for each pair {i,j} of nodes, an edge-connectivity requirement r(ij). The goal is to find a minimum-coir network using the available links and satisfying the requirements. Our algorithm outputs a solution whose cost is within 2[log(2)(r + 1)] of optimal, where r is the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial minmax approximate equality relating minimum-cost networks to maximum packings of certain kinds of cuts. As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic network.