**Abstract :**Localized topology control is attractive for obtaining reduced network graphs with desirable features such as sparser connectivity and reduced transmit powers. In this paper, we focus on studying how to prolong network lifetime in the context of localized topology control for wireless multi-hop networks. For this purpose, we propose an energy efficient localized topology control algorithm. In our algorithm, each node is required to maintain its one-hop neighborhood topology. In order to achieve long network lifetime, we introduce a new metric for characterizing the energy criticality status of each link in the network. Each node independently builds a local energy-efficient spanning tree for finding a reduced neighbor set while maximally avoiding using energy-critical links in its neighborhood for the local spanning tree construction. We present the detailed design description of our algorithm. The computational complexity of the proposed algorithm is deduced to be O(mlog n), where m and n represent the number of links and nodes in a node’s one-hop neighborhood, respectively. Simulation results show that our algorithm significantly outperforms existing work in terms of network lifetime.

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