Traffic Engineering (TE) is a discipline aiming at optimizing internet routing protocols. Segment Routing (SR) was recently introduced by the SPRING and IPv6 working groups of the IETF to tackle TE. In a segment routed network, an ingress node may prepend a header to packets that contain a list of segments, which are instructions that are executed on subsequent nodes in the network. In this talk, we introduce the notion of forward graph and extend it in the context of SR. We study theoretical properties of forward graphs and derive a pre-processing technique allowing to eliminate more than 90 % of the paths on realistic instances. These pre-processing techniques are made very efficient by the use of adequate data structures to represent the forward graphs. We also show with an extensive set of numerical experiments that the pre-processed models can be solved by state-of-the-art solvers without the help of column generation.