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A cut vertex is defined as a network node whose removal increases the number of network components. Failure of a cut vertex disconnects a network component and downgrades the network performance. Overlay networks are resilient to the failure of random nodes, but cut vertices that have been observed in real-world overlay traces make the network very vulnerable to well-constructed and targeted attacks. Traditional methods of detecting cut vertices are centralized and are very difficult, if not impossible, to be applied to large-scale and highly dynamic overlay networks. We aim to provide a practical solution by proposing a distributed mechanism that detects the cut vertices and neutralizes them to noncut vertices before they fail. The proposed mechanism not only minimizes the possibility of network decomposition on the cut vertex failure but also offloads the traffic that is handled by the cut vertices. We prove that our proposed method can correctly identify the cut vertices. We evaluate the performance of our design through trace-driven simulations. The results show that our method can successfully locate all cut vertices in the network and greatly offload the traffic processed by cut vertices.