TY - JOUR

T1 - Optimal preemptive scheduling for general target functions

AU - Epstein, Leah

AU - Tassa, Tamir

N1 - Funding Information:
∗Corresponding author. E-mail addresses: lea@math.haifa.ac.il (L. Epstein), tamirta@openu.ac.il (T. Tassa). 1Research supported by Israel Science Foundation (Grant no. 250/01).

PY - 2006/2/1

Y1 - 2006/2/1

N2 - We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and m≤n 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 [Preemptive scheduling of uniform processor systems, J. ACM (1978) 25(1) 92-101] and later Shachnai et al. [Minimizing makespan and preemption costs on a system of uniform machines, in: Proceedings of the Tenth Annual European Symposium on Algorithms (ESA2002), 2002, pp. 859-871.] 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.

AB - We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and m≤n 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 [Preemptive scheduling of uniform processor systems, J. ACM (1978) 25(1) 92-101] and later Shachnai et al. [Minimizing makespan and preemption costs on a system of uniform machines, in: Proceedings of the Tenth Annual European Symposium on Algorithms (ESA2002), 2002, pp. 859-871.] 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.

KW - Mathematical programming

KW - Optimization

KW - Preemptive scheduling

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=27844512359&partnerID=8YFLogxK

U2 - 10.1016/j.jcss.2005.08.002

DO - 10.1016/j.jcss.2005.08.002

M3 - Article

AN - SCOPUS:27844512359

VL - 72

SP - 132

EP - 162

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

IS - 1

ER -