Experimental results of a coarse-grained parallel algorithm for spanning tree and connected components

Dehne et al. present a BSP/CGM algorithm for computing a spanning tree and the connected components of a graph, that requires O(log p) communication rounds, where p is the number of processors. It requires the solution of the Euler tour problem which in turn is based on the solution of the list ranking problem. In this paper we present experimental results of a parallel algorithm that does not depend on the solution of the Euler tour or the list ranking problem. The proposed algorithm has the practical advantage of avoiding the list ranking computation and is based on the integer sorting algorithm which can be implemented efficiently on the BSP/CGM model. We implemented the proposed algorithm on a Beowulf cluster and on a grid running the InteGrade middleware. We obtained encouraging albeit modest speedup on a small Beowulf cluster and expect good speedups on the grid for larger size graphs and clusters.