We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard and that RoundRobin, the algorithm in which the sensors take turns covering the entire region, has a tight approximation guarantee of 3. Moreover, we show that the more general class of duty cycle algorithms, in 2 which groups of sensors take turns covering the entire region, can do no better. We present similar results for the more general Strip Cover problem, in which each radius may be set finitely-many times. Finally, we give an O(n2 log n)-time optimization algorithm for the related Set Radius Strip Cover problem, in which sensors must be activated immediately.
wireless sensor networks, strip cover, barrier coverage, network lifetime
Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.
Bar-Noy, Amotz; Baumer, Benjamin; and Rawitz, Dror, "Set It and Forget It: Approximating the Set Once Strip Cover Problem" (2015). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.