When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks
AgrawalAjit
KleinPhilip
RaviRamamoorthi
1987
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<sub>ij</sub>. The goal is to find a minimum-cost network using the available links and satisfying
the requirements. Our algorithm outputs a solution whose cost is within 2[log<sub>2</sub>(r + 1)] of optimal, where r is
the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial min-max
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.