Sara Mattia

A polyhedral study of the capacity formulation of the multilayer network design problem

A multilayer network is a hierarchical network where each layer is built using the components of the previous one. Optical networks are an example of two layered networks. The multilayer network design problem consists of installing minimum cost integer capacities on the edges of all the layers so that a set of demands can be routed on the network. In this article, two versions of the optical network design problem are studied, and polyhedral results for the corresponding capacity formulations are presented. We also show how to extend the results to a network with an arbitrary number of layers.

The cut property under demand uncertainty

We consider the robust network design problem, which consists of choosing capacities for the edges of a graph so that a set of uncertain traffic demands can be routed. The scope of the paper is to study the robust cut property RCP, that is, we investigate when the cut inequalities are sufficient to guarantee a feasible routing under demand uncertainty. We provide conditions that ensure the RCP. We discuss the generalization to the problem with uncertain demands of the results that are known for the problem without uncertainty.

Survivable green traffic engineering with shared protection

This article focuses on the problem of minimizing the energy consumption in a resilient telecommunications network. For each demand, an edge-disjoint pair of paths (primary and backup) must be provided and the shared protection scheme is used. The energy consumption is due only to edges used in the no-fault scenario, but both primary and backup paths contribute to capacity consumption. We propose a projected formulation for the problem and show its effectiveness by comparing it with the complete formulation. We propose valid inequalities for both formulations. We evaluate the performances of the proposed formulations and valid inequalities through computational tests. Furthermore, we investigate the relationship between the shared and the dedicated protection version of the problem.

The cut condition for robust network design

Abstract We consider the Robust Network Design problem, i.e. the problem of dimensioning the capacities on the edges of a graph to serve point-to-point traffic demands subject to uncertainty. The scope of the paper is to investigate when the cut condition is sufficient to guarantee the feasibility for such problem.