In communication-denied or contested environments, Line-of-Sight (LoS) communication (e.g free space optical communication using infrared or visible light) becomes one of the most reliable and efficient ways to send information between geographically scattered mobile units. In this paper, we consider the problem of planning optimal locations and trajectories for a group of autonomous vehicles to see a set of units that are dispersed in an environment with obstacles. The contributions of the paper are the following: 1) We propose centralized and distributed algorithms to verify that the vehicles and units form a connected network through LoS; 2) We present an algorithm that can maintain visibility-based connectivity, if possible, by relocating a single vehicle; and 3) We study the computational