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An Optimal Distributed Ear Decomposition Algorithm with Applications to Biconnectivity and Outerplanarity Testing
February 2000 (vol. 11 no. 2)
pp. 110-118

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.

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Index Terms:
Distributed algorithm, message complexity, ear decomposition, biconnectivity testing, outerplanarity testing, depth first search.
Citation:
Art Kazmierczak, Sridhar Radhakrishnan, "An Optimal Distributed Ear Decomposition Algorithm with Applications to Biconnectivity and Outerplanarity Testing," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 2, pp. 110-118, Feb. 2000, doi:10.1109/71.841748
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