Optimal sleep-wakeup algorithms for barriers of wireless sensors

The problem of sleep wakeup has been extensively studied for the full coverage model, where every point in the deployment region is covered by some sensor. Since the sleep-wakeup problem is NP-Hard for this model, several heuristics exist. For the model of barrier coverage, however, where sensors are deployed to form an impenetrable barrier for detecting moving objects (a flagship application of wireless sensor networks), design of an optimal sleep-wakeup algorithm is open. In this paper, we solve this open problem by proposing optimal algorithms not only for the often-used case of equal lifetime but also for the much harder case when sensor lifetimes are different. We prove the optimality of both algorithms. Our algorithms can be used to maintain not just barrier coverage but fault tolerant connectivity, as well, while maximizing the network lifetime. We use simulation to show that for random deployments, even when a minimal number of sensors have been deployed, our optimal algorithms can increase the network lifetime by 500% (from 10 weeks to more than a year). Finally, we show that using our optimal algorithms increases the network lifetime six times longer than that achievable using an existing sleep wake-up algorithm called Randomized Independent Sleeping (RIS).