Computing connected components on parallel computers

We present a parallel algorithm which uses n 2 processors to find the connected components of an undirected graph with n vertices in time O (log 2 n ). An O (log 2 n ) time bound also can be achieved using only n ⌈ n /⌈log 2 n ⌉⌉ processors. The algorithm can be used to find the transitive closure of a symmetric Boolean matrix. We assume that the processors have access to a common memory. Simultaneous access to the same location is permitted for fetch instructions but not for store instructions.