Abstract
P k|fix|C max problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP-hard problem when k⩾ 3. This paper focuses on the case of k=3. Some new observations and new techniques for P 3|fix|C max problem are offered. The concept of semi-normal schedulings is introduced, and a very simple linear time algorithm Semi-normal Algorithm for constructing semi-normal schedulings is developed. With the method of the classical Graham List Scheduling, a thorough analysis of the optimal scheduling on a special instance is provided, which shows that the algorithm is an approximation algorithm of ratio of 9/8 for any instance of P 3|fix|C max problem, and improves the previous best ratio of 7/6 by M.X. Goemans.
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Foundation item: The National Natural Science Foundation of China(No. 69928201); The Changjiang Scholar Reward Project.
Biography of the first author: CHEN Song-qiao, professor, born in 1940, majoring in software engineering.
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Chen, Sq., Huang, Jg. & Chen, Je. Approximation algorithm for multiprocessor parallel job scheduling. J Cent. South Univ. Technol. 9, 267–272 (2002). https://doi.org/10.1007/s11771-002-0040-0
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DOI: https://doi.org/10.1007/s11771-002-0040-0