TY - CHAP

T1 - Optimal Preemptive Scheduling for General Target Functions

AU - Epstein, Leah

AU - Tassa, Tamir

N1 - Funding Information:
∗Corresponding author. E-mail addresses: [email protected] (L. Epstein), [email protected] (T. Tassa). 1Research supported by Israel Science Foundation (Grant no. 250/01).

PY - 2004/1/1

Y1 - 2004/1/1

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 [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.

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 [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.

UR - http://www.scopus.com/inward/record.url?scp=35048831536&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-28629-5_43

DO - 10.1007/978-3-540-28629-5_43

M3 - Chapter

AN - SCOPUS:35048831536

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 562

EP - 573

BT - Mathematical Foundations of Computer Science 2004

A2 - Fiala, Jirí

A2 - Kratochvíl, Jan

A2 - Koubek, Vá clav

PB - Springer Verlag

ER -