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A primal-dual approximation algorithm for generalized Steiner network problems. (English) Zbl 0838.90133
Summary: 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 $$2k$$ of optimal. Our algorithm is primal-dual and shows the importance of this technique in designing approximation algorithms.

##### MSC:
 90C35 Programming involving graphs or networks 90C10 Integer programming
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##### References:
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