Solving Nonlinear Covering Problems Arising in WLAN Design

Wireless Local Area Networks (WLANs) are widely used for cable replacement and wireless Internet access. Since the medium access control (MAC) scheme of WLANs has a strong influence on network performance, it should be accounted for in WLAN design. This paper presents AP location models that optimize a network performance measure specific for the MAC scheme of WLANs, which represents the efficiency in sharing the wireless medium. For these models, we propose a solution framework based on an effective integer-linear programming Dantzig-Wolfe reformulation. This framework is applicable to any nonlinear covering problem where the objective function is a sum of contributions over the groundset elements (users in WLANs). Extensive computational results show that our solution strategy quickly yields optimal or near-optimal solutions for WLAN design instances of realistic size.