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In this paper we propose an algorithm FAKNN for optimizing approximate k-NN queries in WSNs. We assign an empirical value range to each sensor node according to its samples. It is proved in this paper that in once query if all the sensed values are within their corresponding empirical value range, at most k+1 sensor nodes need to be visited for the determination of k-NN query result. However, it is unavoidable that some sensed data will go out of their empirical range. So, we introduce the probability model into FAKNN. It is a tradeoff between the result accuracy and the query cost. We make several simulative experiments to validate the performance of the FAKNN algorithm.