Minimizing the maximum sensor movement for barrier coverage in the plane

Border surveillance for intrusion detection is an important application of wireless sensor networks. Given a set of mobile sensors and their initial positions, how to move these sensors to a region border to achieve barrier coverage energy-efficiently is challenging. In this paper, we study the 2-D MinMax barrier coverage problem of moving n sensors in a two-dimensional plane to form a barrier coverage of a specified line segment in the plane while minimizing the maximum sensor movement for the sake of balancing battery power consumption. Previously, this problem was shown to be NP-hard for the general case. It was an open problem whether the problem is polynomial-time solvable for the case when sensors have a fixed number of sensing ranges. We study a special case of great practical significance that the sensors have the same sensing range and present an O(n³ log n) time algorithm. Our algorithm computes a permutation of the left and right endpoints of the moving ranges of all the sensors forming a barrier coverage and minimizes the maximum sensor movement distance by characterizing permutation switches that are critical. To the best of our knowledge, this is the first result for solving the 2-D MinMax barrier coverage problem for the case that all sensors have a uniform sensing range.