Practical parallel algorithms for minimum spanning trees

We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m/n⩾p, where p is the number of processors. For this case, we show that simple algorithms with data-independent communication patterns are efficient both in theory and in practice. The algorithms are evaluated theoretically using Valiant´s (1990) BSP model of parallel computation and empirically through implementation results