Finding the connected components of an undirected graph G = (V; E) on n = jV j vertices and m = jEj edges is a fundamental computational problem. The best known parallel algorithm for the CREW PRAM model runs in O(log 2 n) time using n 2 = log 2 n processors 6, 15]. For the CRCW PRAM model, in which concurrent writing is permitted, the best known algorithm runs in O(log n) time using slightly more than (n + m)= log n processors 26, 9, 5]. Simulating this algorithm on the weaker CREW model increases its running time to O(log 2 n) 10, 19, 29] . We present here a simple algorithm that runs in O(log 3=2 n) time using n + m CREW processors. Finding an o(log 2 n) parallel connectivity algorithm for this model was an open problem for many years.
In a breakthrough work, Johnson and Metaxas REF presented a CREW algorithm running in O(log 3 2 n) time using n + m processors.
Connected Components in O (log^3/2 n) Parallel Time for the CREW PRAM
J. Comput. Syst. Sci.
Computer Science