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In this paper, we propose a new multiple-sink positioning problem in wireless sensor networks to best support real-time applications. We formally define this problem as the k -Sink Placement Problem ( k -SPP) and prove that it is APX-complete. We show that an existing approximation algorithm for the well-known k -center problem is a constant factor approximation of k -SPP. Furthermore, we introduce a new greedy algorithm for k -SPP and prove its approximation ratio is very near to the best achievable, 2. Via simulations, we show our algorithm outperforms its competitor on average.