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Spatial query execution is an essential functionality of a sensor network. Redundancy within a sensor network can be exploited to reduce the communication cost incurred in execution of such queries. Any reduction in communication cost would result in an efficient use of battery energy, which is very limited in sensors. One approach to reduce the communication cost of a query is to self-organize the network, in response to a query, into a topology that involves only a small subset of the sensors sufficient to process the query. In this paper, we design an efficient algorithm for the above problem of self-organization of a sensor network into an optimal logical topology, to reduce energy consumption, in response to a query. We introduce the EEDSOSC algorithm, a new Energy Efficient Distributed Selforganization approximation algorithm for Optimal Sensor Cover that produces a near-Optimal Sensor Cover with minimum consumed energy, minimum connected sensor cover and less message communication overhead. The performance of algorithm is tested for both dense and sparse sensor networks. Through extensive simulations, we have shown that our designed technique result in substantial energy savings in a sensor network. Moreover, experiments have been conducted on networks with different sensors transmission radius, different query sizes, and different network configurations. All experimental tests are evaluated using simulations and the experimental results showed that the proposed approach results in a significant communication cost reduction and an energy efficient near-optimal connected sensor cover. Compared with other techniques, the results demonstrated a significant improvement of the proposed technique in terms of energy efficient query cover with lower communication cost. [ABSTRACT FROM AUTHOR]