The parallel complexity of tree embedding problems

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(n4.5)-processor O(log3n) time randomized algorithm for determining whether there is a topological embedding of one tree in another and an O(n4.5)-processor O(log3n 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.