A distributed algorithm for finding an ear decomposition of an asynchronous communication network with n nodes and m links is presented in this paper. At the completion of the algorithm either the ears are correctly labeled or the nodes are informed that there exists no ear decomposition. First we present a novel algorithm to check the existence of an ear decomposition which uses O(m) messages. We also present two other algorithms, one which is time-optimal and the other which is message-optimal to determine the actual ears and their corresponding numbers after determining the existence of an ear decomposition.
Sridhar Hannenhalli, Kalyan S. Perumalla, N. Chand