Optimal Randomized Erew Pram Algorithms for Nding Spanning Forests and for Other Basic Graph Connectivity Problems

We present the rst randomized O(logn) 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, and nding Euler tours in Eulerean graphs. For other problems such as nding an ear decomposition , nding an open ear decomposition, nding a strong orientation, and nding an st-numbering we get optimal randomized CREW PRAM algorithms.