When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks

Ajit Agrawal, Philip Klein, R. Ravi
1995 SIAM journal on computing (Print)  
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 Tij. 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 lg R of optimal, where R is the highest requirement value. In the course of proving the performance
more » ... arantee, 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.
doi:10.1137/s0097539792236237 fatcat:hmehrhjj6nfjlnvj35ypnh3hde