Building uniformly random subtrees

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Abstract

We prove the existence of, and describe, a (random) process which builds subtrees of a rooted d-branching tree one node at a time, in such a way that the subtree created at stage n is precisely a uniformly random subtree of size n. The union of these subtrees is a “uniformly random” infinite subtree, which we describe and generate in several ways. Generalization to generation of other combinatorial structures is also considered. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004

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