Wireless communication and sensor networks have been widely employed in our daily life. Sensing-range characteristics, inter-nodal connectivity, and communication capacity are critical factors in providing reliable quality-of-service. Placement of sensors or access-points indoors is always critical to the effectiveness of a wireless communication/sensor network. In this paper, we would like to investigate the important classical sensor/access-point placement problem in the discrete-graph domain. Instead of the conventional trial-and-error approach upon rigorous quality-of-service measurements, we study the sensor/access-point coverage-area maximization problem over visibility graphs and then design a new graph-theoretical approach to deal with it. This new approach just takes the bird's eye view of an indoor geometry (floor plan) as the only necessary input information and does not rely on any quality-of-service measurement. Thus, the crucial coverage-area maximization problem for sensor/access-point placement can be tackled algorithmically. Our new approach can be applied for indoor geometries as arbitrary polygons, either convex or nonconvex.