Optimal Non-preemptive Semi-online Scheduling on Two Related Machines

  • Leah Epstein
  • Lene M. Favrholdt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2420)


We consider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q ≥ 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio 1/4(1 + √17) ≈ 1.28 overall, but does not have optimal competitive ratio for every value of q. We determine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.


Input Sequence Competitive Ratio Speed Ratio Identical Machine Online Schedule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Leah Epstein
    • 1
  • Lene M. Favrholdt
    • 2
  1. 1.The Interdisciplinary CenterSchool of Computer ScienceHerzliyaIsrael
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark

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