Buy‐at‐Bulk Network Design with Protection

We consider approximation algorithms for buy‐at‐bulk network design, with the additional constraint that demand pairs be protected against a single edge or node failure 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. We obtain the first nontrivial approximation algorithms for buy‐at‐bulk network design in the 1 + 1 model for both edge and node‐disjoint protection requirements. Our results are for the single‐cable cost model, which is prevalent in optical networks. More specifically, we present a constant‐factor approximation for the single‐sink case and a polylogarithmic factor approximation for the multicommodity case. These results are of interest for practical applications and also suggest several new challenging theoretical problems.