Optimal Parallel Algorithms for Testing Isomorphism of Trees and Outerplanar Graphs

We show that isomorphism of trees and outerplanar graphs can be tested in O(log n) time with n/log(n) processors on a CRCW PRAM and in O(log2n) time with n/log2n processors on an EREW PRAM. This gives the first optimal parallel algorithm for the isomorphism testing for a nontrivial class of graphs. We give also an optimal parallel algorithm for the equivalence of expressions.

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