Abstract
We consider the problem of scheduling jobs on a single machine with preemption, when the server is allowed to reject jobs at some penalty. We consider minimizing two objectives: total flow time and total job-idle time (the idle time of a job is the flow time minus the processing time). We give 2-competitive online algorithms for the two objectives and extend some of our results to the case of weighted flow time and machines with varying speeds. We also give a resource augmentation result for the case of arbitrary penalties achieving a competitive ratio of \(O(\frac{1}{\epsilon}({\rm log} W + {\rm log} C)^2)\) using a (1 + ε) speed processor. Finally, we present a number of lower bounds for both the case of uniform and arbitrary penalties.
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References
Smith, W.: Various optimizers for single stage production. Naval Research Logistics Quarterly 3, 59–66 (1956)
Chekuri, C., Khanna, S.: Approximation schemes for preemptive weighted flow time. In: ACM Symposium on Theory of Computing (STOC) (2002)
Chekuri, C., Khanna, S., Zhu, A.: Algorithms for weighted flow time. In: STOC (2001)
Bansal, N., Dhamdhere, K.: Minimizing weighted flow time. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 508–516 (2003)
Becchetti, L., Leonardi, S., Spaccamela, A.M., Pruhs, K.: Online weighted flow time and deadline scheduling. In: Goemans, M.X., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) RANDOM 2001 and APPROX 2001. LNCS, vol. 2129, pp. 36–47. Springer, Heidelberg (2001)
Borodin, A., El-Yaniv, R.: On-Line Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L.: Multiprocessor scheduling with rejection. In: ACM-SIAM Symposium on Discrete Algorithms, SODA (1996)
Seiden, S.S.: Preemptive multiprocessor scheduling with rejection. Theoretical Computer Science 262, 437–458 (2001)
Hoogeveen, H., Skutella, M., Woeginger, G.: Preemptive scheduling with rejection. In: European Symposium on Algorithms (2000)
Engels, D., Karger, D., Kolliopoulos, S., Sengupta, S., Uma, R., Wein, J.: Techniques for scheduling with rejection. In: European Symposium on Algorithms, pp. 490–501 (1998)
Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications. Academic Press, London (1979)
Hardy, G., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. JACM 47, 617–643 (2000)
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Bansal, N., Blum, A., Chawla, S., Dhamdhere, K. (2003). Scheduling for Flow-Time with Admission Control. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_7
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DOI: https://doi.org/10.1007/978-3-540-39658-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20064-2
Online ISBN: 978-3-540-39658-1
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