Finding minimum spanning forests in logarithmic time and linear work using random sampling
Richard Cole, Philip N. Klein, Robert Endre Tarjan · 1996
We describe a randomized CRCW PRAM algorithm that finds a minimum spanning forest of an n-vertex graph in O(log n) time and linear work. This shaves a factor of 2 log n off the best previous running time for a linear-work algorithm. The novelty in our approach is to divide the computation into two phases, the first of which finds only a partial solution. This idea has been used previously in parallel connected components algorithms. 1 Introduction We describe the first work-optimal minimum spanning forest (MSF) algorithm that runs in O(log n) time. The algorithm uses a random-sampling technique previously used by Karger, Klein, and Tarjan in a sequential linear-time algorithm and by Cole, Klein, and Tarjan in a parallel algorithm. These previous algorithms have the following form. Choose a random subset of edges, and recursively calculate the MSF of the sample graph, the graph consisting of the chosen edges. Use the recursively calculated minimum spanning forest to identify edges ...