Another Pram Algorithm for Finding Connected Components of Sparse Graphs

We present an algorithm which exploits a new approach to the problem of nding the connected components of an undirected graph, CCug for short, with v vertices and e edges. The algorithm has depth O(log 2 (e)) 1 on a CREW PRAM using e processors, hence its cost is not aaected by the number v of graph vertices. This makes the algorithm the one with best speedup and best cost for CCug on highly sparse graphs. On dense graphs conversely, its performance is comparable to the one of the algorithm in 12] and a little worse than the one in 5]. A variant of the algorithm with the same bound but running on the EREW model is also included. The algorithm can be used to nd the transitive closure of binary, symmetric relations. In this case e is the number of axioms and v is the range of the relation.