Generating random spanning trees more quickly than the cover time

Introduction It is widely known how to generate random spanning trees of an undirected graph. Broder showed how at FOCS [6], and Aldous too found the algorithm [2]. Start at any vertex and do a simple random walk on the graph. Each time a vertex is first encountered, mark the edge from which it was discovered. When all the vertices are discovered, the marked edges form a random spanning tree. This algorithm is easy to code up, has small running time constants, and has a nice proof that it generates