Scheduling parallel tasks on an unbounded number of completely connected processors when communication overhead is taken into account is NP-complete. Assuming that task duplication is not allowed, the authors propose a fast heuristic algorithm, called the dominant sequences clustering (DSC) algorithm, for this scheduling problem. The DSC algorithm is superior to several other algorithms from the literature in terms of both computational complexity and parallel time. The authors present experimental results for scheduling general directed acyclic task graphs (DAGs) and compare the performance of several algorithms. Moreover, they show that DSC is optimum for special classes of DAGs such as join, fork, and coarse tree graphs.