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In this paper novel optimization models are proposed for planning Wireless Mesh Networks (WMNs), where the objective is to minimize the network installation cost while providing full coverage to wireless mesh clients. Our mixed integer linear programming models allow to select the number and positions of mesh routers and access points, while accurately taking into account traffic routing, interference, rate adaptation, and channel assignment. We provide the optimal solutions of three problem formulations for a set of realistic-size instances (with up to 60 mesh devices) and discuss the effect of different parameters on the characteristics of the planned networks. Moreover, we propose and evaluate a relaxation-based heuristic for large-sized network instances which jointly solves the topology/coverage planning and channel assignment problems. Finally, the quality of the planned networks is evaluated under …