Approximation algorithm for multiprocessor parallel job scheduling
Pk|fix|Cmax 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 P3|fix|Cmax 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 P3|fix|Cmax problem, and improves the previous best ratio of 7/6 by M.X. Goemans.
Key wordsmultiprocessor parallel job scheduling approximation algorithm NP-hard problem
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- Amoura A K, Bampis E, Kenyon C, et al. Scheduling independent multiprocessor tasks[A]. In: Burkard R, Woeginger G J eds. Proc 5th Ann European Symposium on Algorithms. Lecture Notes in Computer Science[C]. Berlin: Springer-Verlag Press, 1997. 1–12.Google Scholar
- Huang J, Chen J, Chen S. A simple linear time approximation algorithm for multi-processor job scheduling on four processors[A]. In: Hsu Tsan Sheng ed. 12th Annual International Symposium on Algorithms and Computation. Lecture Notes in Computer Science [C]. Berlin: Springer-Verlag Press, 2000, 1969: 60–71.Google Scholar