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Due to their low cost and small form factors, a large number of sensor nodes can be deployed in redundant fashion in dense sensor networks. The availability of redundant nodes increases network lifetime as well as network fault tolerance. It is, however, undesirable to keep all the sensor nodes active at all times for sensing and communication. An excessive number of active nodes lead to higher energy consumption and it places more demand on the limited network bandwidth. We present an efficient technique for the selection of active sensor nodes in dense sensor networks. The active node selection procedure is aimed at providing the highest possible coverage of the sensor field, i.e., the surveillance area. It also assures network connectivity for routing and information dissemination. We first show that the coverage-centric active nodes selection problem is NP-complete. We then present a distributed approach based on the concept of a connected dominating set (CDS). We prove that the set of active nodes selected by our approach provides full coverage and connectivity. We also describe an optimal coverage-centric centralized approach based on integer linear programming. We present simulation results obtained using an ns2 implementation of the proposed technique.