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Since sensor nodes have limited battery power, it is desirable to select a minimum set of working sensor nodes which should be involved in sensing and forwarding data to the sink. In this paper, we propose a topology scheme which selects a minimum set of working nodes in the sensor network field to avoid wasting excessive energy by turning off too many redundant nodes. Our scheme offers a solution for configuring network topology with a minimal number of working nodes. Simulations show that our scheme extends the lifetime of the dense sensor networks, and achieves the desired robust coverage as well as satisfactory connectivity to the sink in an energy efficient fashion. [ABSTRACT FROM AUTHOR]