Abstract
We present the first comprehensive experimental study of online algorithms for Graham’s scheduling problem. In Graham’s scheduling problem, which is a fundamental and extensively studied problem in scheduling theory , a sequence of jobs has to be scheduled on m identical parallel machines so as to minimize the makespan. Graham gave an elegant algorithm that is (2-1/m)-competitive. Recently a number of new online algorithms were developed that achieve competitive ratios around 1.9. Since competitive analysis can only capture the worst case behavior of an algorithm a question often asked is: Are these new algorithms geared only towards a pathological case or do they perform better in practice, too?
We address this question by analyzingthe algorithms on various job sequences. We have implemented a general testing environment that allows a user to generate jobs, execute the algorithms on arbitrary job sequences and obtain a graphical representation of the results. In our actual tests, we analyzed the algorithms (1) on real world jobs and (2) on jobs generated by probability distributions. It turns out that the performance of the algorithms depends heavily on the characteristics of the respective work load. On job sequences that are generated by standard probability distributions, Graham’s strategy is clearly the best. However, on the real world jobs the new algorithms often outperform Graham’s strategy. Our experimental study confirms theoretical results and gives some new insights into the problem. In particular, it shows that the techniques used by the new online algorithms are also interesting from a practical point of view.
Due to space limitations, this extended abstract contains only parts of our results. A full version of the paper can be obtained at http://ls2-www.informatik.uni-dortmund.de/~albers/ or http://www.cs.cmu.edu/~bianca/
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
S. Albers. Better bounds for online scheduling. In Proc. 29th Annual ACM Symposium on Theory of Computing, pages 130–139, 1997.
Y. Bartal, A. Fiat, H. Karlo. and R. Vohra. New algorithms for an ancient schedulingproblem. Journal of Computer and System Sciences, 51:359–366, 1995.
Y. Bartal, H. Karlo. and Y. Rabani. A better lower bound for on-line scheduling. Information Processing Letters, 50:113–116, 1994.
B. Chen, A. van Vliet and G.J. Woeginger. Lower bounds for randomized online scheduling. Information Processing Letters, 51:219–222, 1994.
E.G. Coffman, L. Flatto, M.R. Garey and R.R. Weber, Minimizing expected makespans on uniform processor systems, Adv. Appl. Prob., 19:177–201, 1987.
E.G. Coffman, L. Flatto and G.S. Lueker Expected makespans for largest-first multiprocessor scheduling, Performance’ 84, Elsevier Science Publishers, 491–506, 1984.
E.G. Coffman Jr., G.N. Frederickson and G.S. Lueker. Expected makespans for largest-first sequences of independent tasks on two Processors, Math. Oper. Res., 9:260–266, 1984.
U. Faigle, W. Kern and G. Turan. On the performance of on-line algorithms for particular problems. Acta Cybernetica, 9:107–119, 1989.
D.G. Feitelson and L. Rudolph, editors. Job Scheduling Strategies for Parallel Processing (IPPS 95). Workshop, Santa Barbara, CA, USA, 25. April, 1995: Proceedings, Springer Lecture Notes in Computer Science, Volume 949, 1995.
D.G. Feitelson and L. Rudolph, editors. Job Scheduling Strategies for Parallel Processing (IPPS 96). Workshop, Honolulu, Hawaii, April 16, 1996: Proceedings, Springer Lecture Notes in Computer Science, Volume 1162, 1996.
G. Galambos and G. Woeginger. An on-line scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM Journal on Computing, 22:349–355, 1993.
R.L. Graham. Bounds for certain multi-processinganomalies. Bell System Technical Journal, 45:1563–1581, 1966.
L.A. Hall, D.B. Shmoys and J. Wein. Schedulingto minimize average completion time: O.-line an on-line algorithms. In Proc. 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 142–151, 1996.
R. Jain. The Art of Computer Systems Performance Analysis, Wiley, 1991.
D.R. Karger, S.J. Phillips and E. Torng. A better algorithm for an ancient schedulingproblem. Journal of Algorithms, 20:400–430, 1996.
M.W.P. Savelsbergh, R.N. Uma and J. Wein. An experimental study of LP-based approximation algorithms for scheduling problems. In Proc. 8th ACM-SIAM Symposium on Discrete Algorithms, pages 453–462, 1998.
D.D. Sleator and R.E. Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28:202–208, 1985.
J. Sgall. A lower bound for randomized on-line multiprocessor scheduling, Information Processing Letters, 63:51–55, 1997.
J. Sgall. On-line scheduling. In Online algorithms: The state of the art, A. Fiat and G.J. Woeginger. Springer Lecture Notes in Computer Science, Volume 1224, pages 196–231, 1998.
D. Shmoys, J. Wein and D.P. Williamson. Scheduling parallel machines on-line. SIAM Journal on Computing, 24:1313–1331, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Albers, S., Schröder, B. (2001). An Experimental Study of Online Scheduling Algorithms. In: Näher, S., Wagner, D. (eds) Algorithm Engineering. WAE 2000. Lecture Notes in Computer Science, vol 1982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44691-5_2
Download citation
DOI: https://doi.org/10.1007/3-540-44691-5_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42512-0
Online ISBN: 978-3-540-44691-0
eBook Packages: Springer Book Archive