This paper considers approximation algorithms for buy-at-bulk network design, with the additional constraint that demand pairs be protected against edge or node failures in the network. In practice, the most popular model used in high speed telecommunication networks for protection against failures, is the so-called 1+1 model. In this model, two edge or node-disjoint paths are provisioned for each demand pair. The paper obtains the first non-trivial approximation algorithms for buy-at-bulk network design in the 1+1 model for both edge and node-disjoint protection requirements. The results are for the single-cable cost model, which is prevalent in optical networks. More specifically, the paper presents a constant-factor approximation for the single-sink case, and an O(log3 n) approximation for the multi-commodity case.
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