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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.

90C35 Programming involving graphs or networks
90C10 Integer programming
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