—When a large amount of sensors are randomly deployed into a field, how can we make a sleep/activate schedule for sensors to maximize the lifetime of target coverage in the field? This is a well-known problem, called Maximum Lifetime Coverage Problem (MLCP), which has been studied extensively in the literature. It is a long-standing open problem whether MLCP has a polynomial-time constant-approximation. The bestknown approximation algorithm has performance ratio 1 + ln