IEEE Transactions on Parallel and Distributed Systems
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We present a parallel algorithm based on open ear decomposition to construct an embedding of a graph onto the plane or report that the graph is non-planar. Our parallel algorithm runs on a CRCW PRAM in logarithmic time with a number of processors bounded by that needed for testing graph connectivity and for performing bucket sort. A sequential implementation of our algorithm gives a new linear-time sequential algorithm for planarity testing.