Approximation Algorithms in Batch Processing

  • Xiaotie Deng
  • Chung Keung Poon
  • Yuzhong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)


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.


Completion Time Release Time Total Completion Time Polynomial Time Approximation Scheme Minimum Makespan 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Xiaotie Deng
    • 1
  • Chung Keung Poon
    • 1
  • Yuzhong Zhang
    • 2
  1. 1.Department of Computer ScienceCity University of Hong KongHong KongChina
  2. 2.Institute of Operations ResearchQufu Normal UniversityQufuChina

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