# The parallel complexity of tree embedding problems (extended abstract)

## Abstract

The sequential complexity of various tree embedding problems arises in the recent work by Robertson and Seymour on graph minors; here we consider the parallel complexity of such problems. In particular, we present two CREW PRAM algorithms: an *O*(*n*^{4.5})-processor *O*(log^{3}*n*) time randomized algorithm for determining whether there is a topological embedding of one tree in another and an *O*(*n*^{4.5})-processor *O*(log^{3}*n* log log *n*) time randomized algorithm for determining whether or not a tree with a degree constraint is a minor of a general tree. These algorithms are two examples of a general technique that can be used for solving other problems on trees. One by-product of this technique is an *NC* reduction of tree problems to matching problems.

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