Building Edge-Failure Resilient Networks

We consider the design of resilient networks that are fault tolerant against link failures. Resilience against link failures can be built into the network by providing backup paths, which are used in the eventuality of an edge failure occurring on a primary path in the network. We consider several network design problems in this context; these problems are motivated by the requirements of current high speed optical networks. In all the following problems, the objective is to provide resilience in networks while minimizing the cost incurred. The main problem under consideration in this paper is that of backup allocation: this problem takes as its input an already provisioned primary network and a parameter k, and allocates backup capacity on the edges of the underlying network so that all the demand can be routed even in the presence of k edge failures. We also consider a variant of this problem where the primary network has a tree topology, and it is required that the restored network retains a tree topology. We then address the problem of simultaneous primary and backup allocation: we are given specifications of the traffic to be handled, and the goal is to provision both the primary a