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Minimizing energy consumption is a fundamental requirement when deploying wireless sensor networks. Accordingly, various topology control protocols have been proposed, which aim to conserve energy by turning off unnecessary sensors while simultaneously preserving a constant level of routing fidelity. However, although these protocols can generally be integrated with any routing scheme, few of them take specific account of the issues which arise when they are integrated with geographic routing mechanisms. Of these issues, the dead-end situation is a particular concern. The dead-end phenomenon (also known as the "local maximum” problem) poses major difficulties when performing geographic forwarding in wireless sensor networks since whenever a packet encounters a dead end, additional overheads must be paid to forward the packet to the destination via an alternative route. This paper presents a distributed dead-end free topology maintenance protocol, designated as DFTM, for the construction of dead-end free networks using a minimum number of active nodes. The performance of DFTM is compared with that of the conventional topology maintenance schemes GAF and Span, in a series of numerical simulations conducted using the ns2 simulator. The evaluation results reveal that DFTM significantly reduced the number of active nodes required in the network and thus prolonged the overall network lifetime. DFTM also successfully constructed a dead-end free topology in most of the simulated scenarios. Additionally, even when the locations of the sensors were not precisely known, DFTM still ensured that no more than a very few dead-end events occurred during packet forwarding.