Min-Max Movement of Sink-Based Mobile Sensors in the Plane for Barrier Coverage

Barrier coverage is a long-lasting problem in mobile and wireless sensor networks, particularly for energy-critical applications. Recently, practical applications propose new barrier coverage applications of using sink-based mobile sensors, with the aim of minimizing the maximum energy consumed by sensor movement. In the problem, we are a set of sinks distributed on the plane each of which can emit mobile sensors with an identical radius. The task is to cover a given barrier using the mobile sensors emitted from the sinks, such that the maximum movement of the sensors is minimized. In this paper, we first design an algorithm for optimally solving the problem based on the key observation of the property against the so-called movement parity and tangent equilibrium points between the sinks. Then based on a more sophisticated investigation of the geometric property of an optimum solution, we improve the runtime of the algorithm to O(k) for k being the number of sink stations, attaining possibly the best runtime of the problem.