Complexity of Energy Efficient Localization With the Aid of a Mobile Beacon

Localization is an essential service in wireless sensor networks. Trilateration is a commonly used solution to range-based localization for providing such services. It might be, however, impossible to localize the entire network at once using trilateration due to low connectivity on sparse deployments. In such scenarios, a mobile beacon with a known position is used to move among and locate the nodes with low connectivity to aid trilateration. Given a network graph, finding a minimum energy route traveled by the mobile beacon is a key problem in many real-world applications. We prove in this letter that this problem called mobile assisted trilateration based energy optimum localization is NP-hard. To the best of our knowledge, this is the first such result in an attempt to computationally classify this important problem. We also provide a compact integer linear programming formulation for the problem.