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Tiny, low-cost sensor devices are expected to be failure-prone and hence in many realistic deployment scenarios for sensor networks these nodes are deployed in higher than necessary densities to meet operational goals. In this paper we address the question of how nodes should be managed in such dense sensor deployments so that the network topology formed by the active sensors is able to provide connected-coverage to the entire area of interest and at the same time increase the lifetime of the network. In particular, we propose and study distributed, low-coordination node wakeup schemes to efficiently construct multiple independent (node-disjoint) sensor network topologies to achieve good fault tolerance. We propose and evaluate different distributed, random and pattern-based wakeup policies for sensor nodes to construct connected-covered topologies. Through analysis and simulations we demonstrate that in dense sensor deployment scenarios, these policies can construct near-optimal topologies (within 2.7% of the optimal) with zero coordination between nodes, as long as location information is available at the individual sensor nodes.Based on these observations, we develop and evaluate a few simple distributed, wakeup based topology construction algorithms that can realize similar performance bounds in realistic sensor deployments, with varying node densities. These algorithms differ in terms of the required level of coordination and the use of sensor location information, and generate connected-covered topologies efficiently, with very low message-exchange overhead.