Abstract
We study the scheduling of a set of jobs, each characterised by a release (arrival) time and a processing time, for a batch processing machine capable of running (at most) a fixed number of jobs at a time. When the job release times and processing times are known a-priori and the inputs are integers, we obtained an algorithm for finding a schedule with the minimum makespan. The running time is pseudo-polynomial when the number of distinct job release times is constant. We also ob- tained a fully polynomial time approximation scheme when the number of distinct job release times is constant, and a polynomial time approxi- mation scheme when that number is arbitrary. When nothing is known about a job until it arrives, i.e., the on-line setting, we proved a lower bound of \( (\sqrt 5 + 1)/2 \) on the competitive ratio of any approximation al- gorithm. This bound is tight when the machine capacity is unbounded.
Keywords
- Completion Time
- Release Time
- Total Completion Time
- Polynomial Time Approximation Scheme
- Minimum Makespan
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This research is partially supported by a grant from Hong Kong Research Grant Council and a grant from City University of Hong Kong as well as a grant from Natural Science Foundation of China and Shandong.
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© 1999 Springer-Verlag Berlin Heidelberg
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Deng, X., Poon, C.K., Zhang, Y. (1999). Approximation Algorithms in Batch Processing. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_16
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DOI: https://doi.org/10.1007/3-540-46632-0_16
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