Offline via Tarjan
Given final graph, DFS + low-link finds all bridges in O(V+E). Standard.
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Online via link-cut
Track spanning forest via link-cut. Non-tree edges close cycles → their tree paths not bridges anymore.
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Two-edge-connected components
Contract non-bridge edges → tree. Its edges = bridges. Its nodes = 2-edge-connected components.
Applications
Network reliability. Real-time infrastructure monitoring. Fault tolerance analysis.