Optimal placement of base stations in border surveillance using limited capacity drones

Abstract

Listen

Translate article

Imagine an island modeled as a simple polygon 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 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 P or its exterior (i.e., over water). We present an algorithm that, given 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(n2+Ldn), where L is the length of P. We also present an algorithm that returns an additive ϵ-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.