Tree open ear decomposition has been proposed as a potentially useful technique in parallel graph algorithms. We present an efficient parallel algorithm implementing depth-first search in a graph, given its tree open ear decomposition. The algorithm runs in O( log n) time with O(m) processors on the CREW PRAM, where m is the number of edges in the graph. We also show that the problem of computing such a decomposition is NP-complete, demonstrating the limited utility of the technique.
Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms
