Scheduling Precedence Graphs in Systems with Interprocessor Communication Times

The problem of nonpreemptively scheduling a set of rn partially ordered tasks on n identical processors subject to interprocessor communication delays is studied in an effort to minimize the makespan. A new heuristic, called Earliest Task First (ETF), is designed and analyzed. It is shown that the makespan wEx-generated by ETF always satisfies to Eq.. (2 1/n wopti) + C, where Wopti) is the optimal makespan without considering communication delays and C is the communication requirements over some immediate predecessor-immediate successor pairs along one chain. An algorithm is also provided to calculate C. The time complexity of Algorithm ETF is O(nm2).