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Subtree Isomorphism is in Random NC

Gibbons, Phillip B.
Karp, Richard M.
Miller, Gary L.
Soroker, Danny
Technical Report Identifier: CSD-87-389
December 2, 1987

Abstract: Given two trees, a guest tree G and a host tree H, the subtree isomorphism problem is to determine whether there is a subgraph of H that is isomorphic to G. We present a randomized parallel algorithm for finding such an isomorphism, if it exists. The algorithm runs in time O(log^3 n) on a CREW PRAM, where n is the number of nodes in H. Randomization is used (solely) to solve each of a series of bipartite matching problems during the course of the algorithm. We demonstrate the close connection between the two problems by presenting a log space reduction from perfect bipartite matching to subtree isomorphism. Finally, we present some techniques to reduce the number of processors used by the algorithm.