We show that face routing, the well-known local routing algorithm for plane graphs introduced by Kranakis and Urrutia, does not in fact succeed for embedded graphs on the torus or higher genus surfaces (contrary to conjecture). We then describe a generalization of face routing, and prove that this algorithm does provide a local routing algorithm for arbitrary graphs embedded in the torus. Finally we discuss extension of this type of algorithm to surfaces of genus g, describing the problems encountered in this setting.
展开▼
