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Clustering is vital for lengthening the lives of resource-constrained wireless sensor nodes. In this work, we propose a cluster-based energy-efficient router placement scheme for wireless sensor networks, where the K-means algorithm is used to select the initial cluster headers and then a cluster header with sufficient battery energy is selected within each cluster. The performance of the proposed scheme was evaluated in terms of the energy consumption, end-to-end delay, and packet loss. Our simulation results using the OPNET simulator revealed that the energy consumption of our proposed scheme was better than that of the low-energy adaptive clustering hierarchy, which is known to be an energy-efficient clustering mechanism. Furthermore, our scheme outperformed low-energy adaptive clustering hierarchy in terms of the end-to-end delay, throughput, and packet loss rate.