Parallel Open Ear Decomposition with Applications to Graph Biconnectivity and Triconnectivity

This report deals with a parallel algorithmic technique that has proved to be very useful in the design of eecient parallel algorithms for several problems on undirected graphs. We describe this method for searching undirected graphs, called \open ear decomposition", and we relate this decomposition to graph biconnectivity. We present an eecient parallel algorithm for nding this decomposition and we relate it to a sequential algorithm based on depth-rst search. We then apply open ear decomposition to obtain an eecient parallel algorithm for testing graph triconnectivity and for nding the triconnnected components of a graph. This material will appear as a chapter in the book, Synthesis of Parallel Algorithms , edited by John Reif, which is to be published by Morgan-Kaufmann.