A primal-dual approximation algorithm for generalized Steiner network problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
An approximation algorithm for minimum-cost vertex-connectivity problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
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We present a general approximation technique for a class of network design problems where we seek a network of minimum cost that satisfies certain communication requirements and is resilient to worst-case single-link failures. Our algorithm runs in $O(n^2 \log n)$ time on a graph ith $n$ nodes and outputs a solution of cost at most thrice the optimum. We extend our technique to obtain approximation algorithms for augmenting a given network so as to satisfy certain communication requirements and achieve resilience to single-link failures. Our technique allows one to find nearly minimum-cost two-connected networks for a variety of connectivity requirements. For example, our result generalizes earlier results on finding a minimum-cost two-connected subgraph of a given edge-weighted graph and an earlier result on finding a minimum-cost subgraph two-connecting a specified subset of the nodes. Using our technique, we can also approximately solve for the first time a two-connected version of the generalized Steiner network problem and a two-connected version of the non-fixed point-to-point connection problem.