Multiprocessor scheduling with interprocessor communication delays

Authors:
Chung-Yee Lee;Jing-Jang Hwang;Yuan-Chieh Chow;Frank D. Anger
Affiliations:
Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA;Department of Management Science, National Chiao-Tung University, Taiwan, R.O.C.;Department of Computer and Information Sciences, University of Florida, Gainesville, FL 32611, USA;Department of Mathematical and Computer Science, Florida Institute of Technology, Melbourne, FL 32901, USA
Venue:
Operations Research Letters
Year:
1988

Citing 3
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Abstract

We consider the problem of scheduling a set of n partially ordered tasks on m identical processors in order to minimize the makespan, where there is a communication delay between any pair of distinct processors. This problem is NP-hard. We provide a heuristic algorithm, call it Earliest Ready Task (ERT) algorithm, to solve the problem. Among all tasks whose parent tasks have been assigned, an ERT algorithm is one that always chooses one task that can be processed earliest. We show that the makespan M generated by ERT algorithm always satisfies M @? (2-1/m)M' + C"c"o"m"m, where M' is the optimal makespan without considering communication delay and C"c"o"m"m is the maximum communication delay in one chain. We will also provide an algorithm to find this chain. The time complexity of implementing the ERT algorithm is O(mn^2).