Joint Routing and Gateway Selection in Wireless Mesh Networks

A family of mathematical programs for both the un- capacitated and capacitated joint gateway selection and routing (U/C-GSR) problem in wireless mesh networks are presented. We detail a reformulation using the shortest path cost matrix (SPM) and prove that it gives the optimal solution when applied to the uncapacitated case but can lead to an arbitrary large optimality gap in the capacitated case. Furthermore, an augmented mathematical program is developed where link capacities are allowed to take values from a discrete set depending on the link distance. In this case, the multi-rate capabilities of WMNs (via, for example, adaptive modulation and coding) can be modeled. Evidence from numerical investigations shows that using the SPM formulation realistic network sizes of WMNs can be solved.