An optimal distributed ear decomposition algorithm with applications to biconnectivity and outerplanarity testing

We present an asynchronous distributed algorithm to determine an ear decomposition of an arbitrary, connected, bidirectional network containing n-nodes and m-links which uses O(m) messages and which can be completed in O(n) time. Using the ear decomposition, we obtain the following results for a distributed network: 1) The distributed ear decomposition algorithm can be used to test biconnectivity, determine biconnected components, find cutpoints and bridges using O(m) messages in O(n) time. 2) The distributed ear decomposition algorithm can be used to test if a biconnected network is outerplanar using O(n) messages in O(n) time, and if the network is outerplanar, the embedding is also given using the same message and time complexity.