Optimal Preemptive Scheduling for General Target Functions

  • Leah Epstein
  • Tamir Tassa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3153)


We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and mn uniformly related machines, one aims at scheduling the jobs to the machines, allowing preemptions but forbidding parallelization, so that a given target function of the loads on each machine is minimized. This problem was studied in the past in the case of the makespan. Gonzalez and Sahni [7] and later Shachnai, Tamir and Woeginger [12] devised a polynomial algorithm that outputs an optimal schedule for which the number of preemptions is at most 2(m–1). We extend their ideas for general symmetric, convex and monotone target functions. This general approach enables us to distill the underlying principles on which the optimal makespan algorithm is based. More specifically, the general approach enables us to identify between the optimal scheduling problem and a corresponding problem of mathematical programming. This, in turn, allows us to devise a single algorithm that is suitable for a wide array of target functions, where the only difference between one target function and another is manifested through the corresponding mathematical programming problem.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Leah Epstein
    • 1
  • Tamir Tassa
    • 2
  1. 1.School of Computer ScienceThe Interdisciplinary CenterHerzliyaIsrael
  2. 2.Department of Mathematics and Computer Science, The Open University, Ramat Aviv, Tel Aviv, and Department of Computer ScienceBen Gurion UniversityBeer ShevaIsrael

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