Shared protection network design: benefits and costs
Network design with Shared Protection is probably the most efficient way to ensure that 100% traffic is routed on the network even in the case of a link failure. Shared Protection (SP) consists of two path for each demand, a working path and a backup path, that are link disjoint w.r.t. each other. If we stopped here, this would be plain old 1+1 protection. However, consider the situation in the figures below: two demands have working paths (in bold) that do not share any edge, while their backup paths to share two edges.
Under the single failure assumption, only one of the two backup paths will be used at any time, which means that the total capacity needed at those two shared edges is equal to the maximum between the two traffic demand volumes.
One way to return a Shared Protection network is to design a 1+1 protection network and then check for all possible shared capacity and reduce the total cost accordingly. However, this is only a heuristic approach, whereby we apply a post-processing step to a solution to a different problem. The real Shared Protection network design problem is more complicated and should provide a better total cost. But how different?
The scope of this project is to compare the post-processing solution with the optimal solution of SP in terms of total network cost.
Data: use the nobel-eu and the atlanta instances found on the sndlib website. As the model is rather difficult for any solver, only consider at most two demands for every node (i.e. every node 
For both instances, compute the optimal value A of a shared protection network and the optimal value B of a non-shared network with a 1+1 protection scheme. Given the optimal solution of the non-shared network, compute the value C of the network cost if we assumed to fix the routing and computed the possible shared capacity on the network. Verify that 