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Wireless sensor networks have posed a number of challenging problems such as localization, deployment and tracking, etc. One of the interesting problems is the calculation of the coverage and exposure paths for the sensor networks.This paper presents a fully localized algorithm to solve the worst coverage problem first introduced by Meguerdichian et al.The nodes of the sensor network cooperate to construct the worst coverage path only by the one-hop neighbor’s information,thus avoiding the massive communication and conserving the energy. The correctness of the proposed algorithm is proved formally under the sensing diminishing model. Moreover, this algorithm can be easily extended to solve the minimal exposure problem with local information as well.