Scheduling Precedence Graphs in Systems with Interprocessor Communication Times

• Published in: SIAM journal on computing Vol. 18; no. 2; pp. 244 - 257
• Main Authors: Hwang, Jing-Jang, Chow, Yuan-Chieh, Anger, Frank D., Lee, Chung-Yee
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.04.1989
• Subjects: Algorithms; Applied sciences; Communication; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; Heuristic; Job shops; Schedules; Scheduling; Software; Multiprocessor; Graph; Integrated planning; Heuristic method; Transmission protocol; Computer system; Distributed system; Modeling; Delay
• ISSN: 0097-5397; 1095-7111
• DOI: 10.1137/0218016

The problem of nonpreemptively scheduling a set of $m$ 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 $\omega _{{\text{ETF}}} $ generated by ETF always satisfies $\omega _{{\text{ETF}}} \leqq ({{2 - 1} / n})\omega _{{\text{opt}}}^{(i)} + C$, where $\omega _{{\text{opt}}}^{(i)} $ 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 $O(nm^2 )$.