Witnessing broad energy‐critical applications of barrier coverage in mobile and wireless sensor networks, emerging practical applications have recently brought a new barrier coverage model which uses sink‐based mobile sensors for covering a given barrier with the aim of prolonging the lifespan of the coverage. In the model, a set of sink stations were distributed on the plane in which each sink can emit mobile sensors with an identical radius. The task is to cover a given line barrier with the emitted mobile sensors, aiming to minimize the maximum movement of the sensors so as to prolong the shortest lifespan among the sensors in coverage. In this paper, we first devise an algorithm for optimally solving the problem based on the properties of the structures called movement parity and tangent equilibrium points between the sinks. Then based on a more sophisticated geometric property of optimum solutions, we improve the runtime to a linear runtime O(k) which attains the possibly optimum runtime of the problem for k being the number of sinks. At last, numerical experiments are carried out to demonstrate the practical performance gain of our algorithms against baselines in literature.

Given a set of sensors distributed on the plane and a set of Point of Interests (POIs) on a line segment, a primary task of the mobile wireless sensor network is to schedule covering the POIs by the sensors, such that each POI is monitored by at least one sensor. For balancing the energy consumption, we study the min-max line barrier target coverage (LBTC) problem which aims to minimize the maximum movement of the sensors from their original positions to their final positions at which the coverage is composed. We first proved that when the radius of the sensors are non-uniform integers, even 1-dimensional LBTC (1D-LBTC), a special case of LBTC in which the sensors are distributed on the line segment instead of the plane, is NP-hard. The hardness result is interesting, since the continuous version of LBTC to cover a given line segment instead of the POIs is known polynomial solvable. Then we present an exact algorithm for LBTC with uniform radius and sensors distributed on the plane, via solving the decision version of LBTC. We argue that our algorithm runs in time O(n2prefixlogn) and produces an optimal solution to LBTC. The time complexity compares favorably to the state-of-art runtime O(n3prefixlogn) of the continuous version which aims to cover a line barrier instead of the targets. Last but not the least, we carry out numerical experiments to evaluate the practical performance of the algorithms, which demonstrates a practical runtime gain comparing with an optimal algorithm based on integer linear programming.

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