Covering Users by a Connected Swarm Efficiently

In this paper we study covering problems that arise in wireless networks with Unmanned Aerial Vehicles (UAVs) swarms. In the general setting we want to place a set of UAVs that should cover a given set of planar users under some constraints and we want to maintain the solution efficiently in a static and dynamic fashion. Specifically, for a set S of n non-negative weighted points in the plane, we consider a set P of m disks (or squares) of radius \(R_{COV}\) where the goal is to place (and maintain under dynamic updates) their location such that the sum of the weights of the points in S covered by disks from P is maximized. In the connected version, we also require that the graph imposed on P should be connected. Moreover, for the static connected version we improve the results from [1] and we obtain a constant factor approximation algorithm. In order to solve our problem under various requirements, we use a variety of techniques including dynamic grid, a reduction to Budgeted Subset Steiner Connected Dominating Set problem, tree partition, and others. We present several simple data structures that maintain an O(1)-approximate solution efficiently, under insertions and deletions of points to/from S where each update operation can be performed in logarithmic time.