Abstract
Consider the classical online scheduling problem where jobs that arrive one by one are assigned to identical parallel machines with the objective of minimizing the makespan. We generalize this problem by allowing the current assignment to be changed whenever a new job arrives, subject to the constraint that the total size of moved jobs is bounded by β times the size of thearriving job.
Our main result is a linear time ‘online approximation scheme’, that is, a family of online algorithms with competitive ratio 1+ε and constant migration factor β(ε), for any fixed ε> 0. This result is of particular importance if considered in the context of sensitivity analysis: While a newly arriving job may force a complete change of the entire structure of an optimal schedule, only very limited ‘local’ changes suffice to preserve near-optimal solutions. We believe that this concept will find wide application in its own right. We also present simple deterministic online algorithms with migration factors β=2 and β=4/3, respectively. Their competitive ratio 3/2 beats the lower bound on the performance of any online algorithm in the classical setting without migration. We also present improved algorithms and similar results for closely related problems. In particular, there is a short discussion of corresponding results for the objective to maximize the minimum load of a machine. The latter problem has an application for configuring storage servers that was the original motivation for this work.
This work was partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT) and by the EU Thematic Network APPOL II, Approximation and Online Algorithms, IST-2001-30012.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Albers, S.: Better bounds for online scheduling. SIAM Journal on Computing 29, 459–473 (1999)
Albers, S.: Online algorithms: a survey. Mathematical Programming 97, 3–26 (2003)
Andrews, M., Goemans, M.X., Zhang, L.: Improved bounds for on-line load balancing. Algorithmica 23, 278–301 (1999)
Azar, Y., Epstein, L.: On-line machine covering. Journal of Algorithms 1, 67–77 (1998)
Bartal, Y., Fiat, A., Karloff, H., Vohra, R.: New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences 51, 359–366 (1995)
Chen, B., van Vliet, A., Woeginger, G.J.: Lower bounds for randomized online scheduling. Information Processing Letters 51, 219–222 (1994)
Fleischer, R., Wahl, M.: Online scheduling revisited. Journal of Scheduling 3, 343–353 (2000)
Garey, M.R., Johnson, D.S.: Strong np-completeness results: Motivation, examples and implications. Journal of the ACM 25, 499–508 (1978)
Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell System Technical Journal 45, 1563–1581 (1966)
Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: Theoretical and practical results. Journal of the ACM 34, 144–162 (1987)
Karger, D.R., Phillips, S.J., Torng, E.: A better algorithm for an ancient scheduling problem. Journal of Algorithms 20, 400–430 (1996)
Rudin III., J.F.: Improved bounds for the on-line scheduling problem. PhD thesis, The University of Texas at Dallas (2001)
Sanders, P.: Algorithms for scalable storage servers. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2004. LNCS, vol. 2932, pp. 82–101. Springer, Heidelberg (2004)
Sanders, P., Sivadasan, N., Skutella, M.: Online scheduling with bounded migration. Research Report MPI-I-2004-1-004, Max-Planck-Institut für Informatik, Saarbrücken, Germany (April 2004)
Schrijver, A.: Theory of Linear and Integer Programming. John Wiley & Sons, Chichester (1986)
Sgall, J.: A lower bound for randomized on-line multiprocessor scheduling. Information Processing Letters 63(1), 51–55 (1997)
Sgall, J.: On-line scheduling — a survey. In: Fiat, A. (ed.) Dagstuhl Seminar 1996. LNCS, vol. 1442, pp. 196–231. Springer, Heidelberg (1998)
Westbrook, J.: Load balancing for response time. J. Algorithms 35(1), 1–16 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sanders, P., Sivadasan, N., Skutella, M. (2004). Online Scheduling with Bounded Migration. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_92
Download citation
DOI: https://doi.org/10.1007/978-3-540-27836-8_92
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22849-3
Online ISBN: 978-3-540-27836-8
eBook Packages: Springer Book Archive