Fault-tolerant coverage with maximum lifetime in wireless sensor networks

Energy efficiency is an important issue in the study of wireless sensor networks. Given a homogeneous set of sensors with unit lifetime and a set of target points, find an active/sleeping schedule for sensors to maximize the lifetime of k-coverage, i.e., the time period during which every target point is covered by at least k active sensors. This is a well known problem in wireless sensor networks concerning with energy efficiency. When k = 1, it is called the maximum lifetime coverage problem which has been proved to have a polynomial-time (4 + ε)-approximation. When k ≥ 2, it is the maximum lifetime fault-tolerant coverage problem. Previous to this work, only in the case k = 2, a polynomial-time (6 + ε)-approximation is found. In this paper, we will make a significant progress by showing that for any positive integer k, there exists a polynomial-time (4 + ε)-approximation, and for k = 1,2, the performance ratio can be improved to (3 + ε).