Section: Application Domains
Telecommunication network design
Network design is a wide research domain arising in railway, highway and telecommunication. Applications in telecoms are very much studied at the moment, a revival due to the arrival of new transfer technologies such as optical fibers. The aim is to conceive cheap and reliable networks with specific requirements on the topology (which links will be created) or the capacity of the links (which amount of information can be in transit on a link at the same time). Sufficient capacities have to be installed to avoid congestion, several paths may have to link given pairs of nodes to ensure transmission in case of breakdown, all this at the cheapest possible cost.
We are actively working on problems arising in network topology design, implementing a survivability condition of the form “at least two paths link each pair of terminals”. We have extended polyhedral approaches to problem variants with specific requirements. In [82] , we deal with the design of so-called SDH/SONET networks, where the links must form cycles of bounded length; bounded length requirements can also come from re-routing restrictions [104] , [67] , [103] . Associated to network design is the question of traffic routing in the network: one needs to check that the network capacity suffices to carry the demand for traffic. The assignment of traffic also implies the installation of specific hardware at transient or terminal nodes. In previous work, we optimized traffic assignment to minimize such installation cost [148] . We now consider the problem that arises when using new wavelength division multiplexing (WDM) technologies that allow to pack more traffic on optical networks. Several streams can be multiplexed, each of them supported by a different wavelength, in an optical signal [40] (Figure 1 illustrates the design of a european multipexed network). We are also working on the problem of measuring traffic in a network through the placement of markers at minimal cost [120] .
