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Motivated by recent developments in wireless sensor networks (WSNs), we present several efficient clustering algorithms for maximizing the lifetime of WSNs, i.e., the duration till a certain percentage of the nodes die. Specifically, an optimization algorithm is proposed for maximizing the lifetime of a single-cluster network, followed by an extension to handle multi-cluster networks. Then we study the joint problem of prolonging network lifetime by introducing energy-harvesting (EH) nodes. An algorithm is proposed for maximizing the network lifetime where EH nodes serve as dedicated relay nodes for cluster heads (CHs). Theoretical analysis and extensive simulation results show that the proposed algorithms can achieve optimal or suboptimal solutions efficiently, and therefore help provide useful benchmarks for various centralized and distributed clustering scheme designs.