Abstract
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.
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References
Alon, N., Azar, Y., Woeginger, G., Yadid, T.: Approximation schemes for scheduling on parallel machines. Journal of Scheduling 1(1), 55–66 (1998)
Coffman Jr., E.G., Lueker, G.S.: Approximation algorithms for extensible bin packing. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 586–588 (2001)
Dell’Olmo, P., Kellerer, H., Speranza, M.G., Tuza, Z.: A 13/12 approximation algorithm for bin packing with extendable bins. Information Processing Letters 65(5), 229–233 (1998)
Dell’Olmo, P., Speranza, M.G.: Approximation algorithms for partitioning small items in unequal bins to minimize the total size. Discrete Applied Mathematics 94, 181–191 (1999)
Ebenlendr, T., Sgall, J.: Optimal and online preemptive scheduling on uniformly related machines. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 199–210. Springer, Heidelberg (2004)
Epstein, L., Sgall, J.: Approximation schemes for scheduling on uniformly related and identical parallel machines. Algorithmica 39(1), 151–162 (2004)
Gonzalez, T., Sahni, S.: Preemptive scheduling of uniform processor systems. Journal of the ACM 25(1), 92–101 (1978)
Hochbaum, D.S., Shanthikumar, J.G.: Convex separable optimization is not much harder than linear optimization. Journal of the ACM 37(4), 843–862 (1990)
Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: using the dual approximation approach. SIAM Journal on Computing 17(3), 539–551 (1988)
Horvath, E.C., Lam, S., Sethi, R.: A level algorithm for preemptive scheduling. Journal of the ACM 24(1), 32–43 (1977)
Liu, J.W.S., Yang, A.T.: Optimal scheduling of independent tasks on heterogeneous computing systems. In: Proceedings ACM National Conference, vol. 1, pp. 38–45. ACM, New York (1974)
Shachnai, H., Tamir, T., Woeginger, G.J.: Minimizing makespan and preemption costs on a system of uniform machines. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 859–871. Springer, Heidelberg (2002)
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Epstein, L., Tassa, T. (2004). Optimal Preemptive Scheduling for General Target Functions. In: Fiala, J., Koubek, V., KratochvÃl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_43
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DOI: https://doi.org/10.1007/978-3-540-28629-5_43
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