A primal-dual approximation algorithm for generalized steiner network problems

We present the first polynomial-time approximation algorithm for finding a minimum-cost subgraph having at least a specified number of edges in each cut. This class of problems includes, among others, the generalized Steiner network problem, also called the survivable network design problem. If k is the maximum cut requirement of the problem, our solution comes within a factor of 2 k of optimal. Our algorithm is primal-dual and shows the importance of this technique in designing approximation algorithms. © 1995 Akadémiai Kiadó.