Summary: Imagine an island modeled as a simple polygon \(\mathcal{P}\) with \(n\) vertices whose coastline we wish to monitor. We consider the problem of building the minimum number of refueling stations along the boundary of \(\mathcal{P}\) in such a way that a drone can follow a polygonal route enclosing the island without running out of fuel. A drone can fly a maximum distance \(d\) between consecutive stations and is restricted to move either along the boundary of \(\mathcal{P}\) or its exterior (i.e., over water). We present an algorithm that, given \(\mathcal{P}\), finds the locations for a set of refueling stations whose cardinality is at most the optimal plus one. The time complexity of this algorithm is \(O(n^2 + \frac{L}{d}n)\), where \(L\) is the length of \(\mathcal{P}\). We also present an algorithm that returns an additive \(\varepsilon\)-approximation for the problem of minimizing the fuel capacity required for the drones when we are allowed to place \(k\) base stations around the boundary of the island; this algorithm also finds the locations of these refueling stations. Finally, we propose a practical discretization heuristic which, under certain conditions, can be used to certify optimality of the results.