An Optimal Distributed Ear Decomposition Algorithm with Applications to Biconnectivity and Outerplanarity Testing

Authors:
Art Kazmierczak;Sridhar Radhakrishnan
Affiliations:
Univ. of Texas at Tyler, Tyler;Univ. of Oklahoma, Norman
Venue:
IEEE Transactions on Parallel and Distributed Systems
Year:
2000

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Abstract

We present an asynchronous distributed algorithm to determine an ear decomposition of an arbitrary, connected, bi-directional 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.