A deterministic parallel algorithm for determining whether two planar graphs are isomorphic is presented. The algorithm needs O(log n) separators that have to be computed one after the other. The running time is T=O(log/sup 3/ n) time for finding separators, and the processors count is n/sup 1.5/ log n/T. It is also shown that every planar graph has a separator, and a parallel algorithm for finding the separator is given.
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