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The adoption of UAVs in communication networks is becoming reality thanks to the deployment of advanced solutions for connecting UAVs and using them as communication relays. However, the use of UAVs introduces novel energy constraints and scheduling challenges in the dynamic management of network devices, due to the need to call back and recharge, or substitute, UAVs that run out of energy. In this paper, we design UAV recharging schemes under realistic assumptions on limited flight times and time consuming charging operations. Such schemes are designed to minimize the size of the fleet to be devoted to a persistent service of a set of aerial locations, hence its cost. We consider a fleet of homogeneous UAVs both under homogeneous and heterogeneous service topologies. For UAVs serving aerial locations with homogeneous distances to a recharge station, we design a simple scheduling, that we name HORR, which we prove to be feasible and optimal, in the sense that it uses the minimum possible number of UAVs to guarantee the coverage of the aerial service locations. For the case of non-evenly distributed aerial locations, we demonstrate that the problem becomes NP-hard, and design a lightweight recharging scheduling scheme, PHERR, that extends the operation of HORR to the heterogeneous case, leveraging the partitioning of the set of service locations. We show that PHERR is near-optimal because it approaches the performance limits identified through a lower bound that we formulate on the total fleet size.