This paper proposes an optimization based approach to multi-UGV surveillance. In particular, we formulate both the minimum time- and connectivity constrained surveillance problems, show NP-hardness of them and propose decomposition techniques that allow us to solve them efficiently in an algorithmic manner. The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a path and such that the time for executing the search in parallel is minimized. Here, the sensor's field of view are assumed to be occluded by the obstacles and limited by a maximal sensor range. The connectivity constrained formulation extends the first by additionally requiring that the information graph induced by the sensors is connected at the time instants when the UGVs stop to perform the surveillance task. The second formulation is relevant to situation when mutual visibility is needed either to transmit the sensor data being gathered, or to protect the team from hostile persons trying to approach the stationary UGVs.