**1. Introduction**

The arrival of the optical fiber allowed for an enormous increase on communication line bandwidth. This naturally led to deploying networks with dispersed topologies, as scarce (even unique) paths linking the diverse sites are enough to fulfill all the requirements regarding data exchanges. Yet dispersed topologies have a problem: the ability of the network to keep all sites connected is affected by the failure of few (even one single) communication links or switch sites. Before the introduction of the optical fiber, topologies were denser; upon failure of few links, there was a probable reduction of throughput, yet keeping all sites connected. With disperse fiber-based designs, the network behaves much more as an "all-ornothing" service; either, it fulfills all requirements of connectivity and bandwidth, or it fails to connect some sites. Therefore, the problem of designing networks with minimal costs and reliability thresholds has since gained relevance.

In view of the above, the networks must continue to be operative even when a component (link or central office) fails. In this context, survivability means that a certain number of pre-established disjoint paths among any pair of central offices must exist. In this case, node-disjoint paths will be required, which show a stronger constraint than the edge-disjunction ones. Assuming that both the links and the nodes have associated certain operation probabilities (elementary reliability), the main objective is to build a minimum-cost sub-network that satisfies the nodeconnectivity requirements. Moreover, its reliability, i.e., the probability that all sites are able to exchange data at a given point in time, ought to surpass a certain lower bound pre-defined by the network engineer. In this way the model takes into account the robustness of the topology to be designed by acknowledging its structure even in probabilistic terms.
