An Optimal Distributed Edge-Biconnectivity Algorithm
  We describe a synchronous distributed algorithm which identifies the edge-biconnected components of a connected network. It requires a leader, and uses messages of size O(log |V|). The main idea is to preorder a BFS spanning tree, and then to efficiently compute least common ancestors so as to mark cycle edges. This algorithm takes O(Diam) time and uses O(|E|) messages. Furthermore, we show that no correct singly-initiated edge-biconnectivity algorithm can beat either bound on any graph by more than a constant factor. We also describe a near-optimal local algorithm for edge-biconnectivity. 
David Pritchard