A Coarse-Grained Parallel Algorithm for Spanning Tree and Connected Components

Computing a spanning tree and the connected components of a graph are basic problems in Graph Theory and arise as subproblems in many applications. 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 a new approach that does not need to solve the Euler tour or the list ranking problem. It still requires O(log p) communication rounds and has the practical advantage of avoiding the list ranking computation. Rather it is based on the integer sorting algorithm which can be implemented efficiently on the BSP/CGM model.