Gateway selection and routing in wireless mesh networks

This paper deals with issues regarding network planning and optimization in multi-hop wireless mesh networks (WMNs). The central focus is on mathematical programming formulations for both the uncapacitated and capacitated joint gateway selection and routing (U/C-GSR) problem in WMNs, which are in general NPNP-complete, when expressed as decision problems. 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. We extend the SPM formulation to the capacitated case and show computationally, by using a lower bound on the optimal solution, that it performs within a small optimality gap. Evidence from numerical investigations shows that, the proposed formulation can dramatically improve the computation time for WMNs with realistic network sizes. Furthermore, a set of extensions to the basic formulation is detailed to allow modeling issues such as multi-rate transmission, restricting the number of hops in each routing sub-tree and declaring unreliable nodes as leaf nodes in the routing tree.