Optimal Randomized EREW PRAM Algorithms for Finding Spanning Forests

We present the rst randomized O(log n) time and O(m+n) work EREW PRAM algorithm for nding a spanning forest of an undirected graph G = (V; E) with n vertices and m edges. Our algorithm is optimal with respect to time, work and space. As a consequence we get optimal randomized EREW PRAM algorithms for other basic connectivity problems such as nding a bipartite partition, nding bridges and biconnected components, nding Euler tours in Eulerian graphs, nding an ear decomposition, nding an open ear decomposition, nding a strong orientation, and nding an st-numbering.