Abstract
We consider online preemptive scheduling of jobs with fixed starting times revealed at those times on m uniformly related machines, with the goal of maximizing the total weight of completed jobs. Every job has a size and a weight associated with it. A newly released job must be either assigned to start running immediately on a machine or otherwise it is dropped. It is also possible to drop an already scheduled job, but only completed jobs contribute their weights to the profit of the algorithm.
In the most general setting, no algorithm has bounded competitive ratio, and we consider a number of standard variants. We give a full classification of the variants into cases which admit constant competitive ratio (weighted and unweighted unit jobs, and C-benevolent instances, which is a wide class of instances containing proportional-weight jobs), and cases which admit only a linear competitive ratio (unweighted jobs and D-benevolent instances). In particular, we give a lower bound of m on the competitive ratio for scheduling unit weight jobs with varying sizes, which is tight. For unit size and weight we show that a natural greedy algorithm is 4/3-competitive and optimal on m = 2 machines, while for a large m, its competitive ratio is between 1.56 and 2. Furthermore, no algorithm is better than 1.5-competitive.
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.
References
Awerbuch, B., Bartal, Y., Fiat, A., Rosén, A.: Competitive non-preemptive call control. In: Proc. of 5th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1994), pp. 312–320 (1994)
Canetti, R., Irani, S.: Bounding the power of preemption in randomized scheduling. SIAM Journal on Computing 27(4), 993–1015 (1998)
Krumke, S.O., Thielen, C., Westphal, S.: Interval scheduling on related machines. Computers & Operations Research 38(12), 1836–1844 (2011)
Faigle, U., Nawijn, W.M.: Note on scheduling intervals on-line. Discrete Appliled Mathematics 58(1), 13–17 (1995)
Fung, S.P.Y., Poon, C.K., Zheng, F.: Online interval scheduling: randomized and multiprocessor cases. Journal of Combinatorial Optimization 16(3), 248–262 (2008)
Fung, S.P.Y., Poon, C.K., Zheng, F.: Improved Randomized Online Scheduling of Unit Length Intervals and Jobs. In: Bampis, E., Skutella, M. (eds.) WAOA 2008. LNCS, vol. 5426, pp. 53–66. Springer, Heidelberg (2009)
Fung, S.P.Y., Poon, C.K., Yung, D.K.W.: On-line scheduling of equal-length intervals on parallel machines. Information Processing Letters 112(10), 376–379 (2012)
Fung, S.P.Y., Poon, C.K., Zheng, F.: Improved randomized online scheduling of intervals and jobs. CoRR abs/1202.2933 (2012)
Woeginger, G.J.: On-line scheduling of jobs with fixed start and end times. Theoretical Computer Science 130(1), 5–16 (1994)
Carlisle, M.C., Lloyd, E.L.: On the k-coloring of intervals. Discrete Appliled Mathematics 59(3), 225–235 (1995)
Epstein, L., Levin, A.: Improved randomized results for the interval selection problem. Theoretical Computer Science 411(34-36), 3129–3135 (2010)
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. Journal of the ACM 47(4), 617–643 (2000)
Koo, C., Lam, T.W., Ngan, T., Sadakane, K., To, K.: On-line scheduling with tight deadlines. Theoretical Computer Science 295, 251–261 (2003)
Seiden, S.S.: Randomized online interval scheduling. Operations Research Letters 22(4-5), 171–177 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Epstein, L., Jeż, Ł., Sgall, J., van Stee, R. (2012). Online Scheduling of Jobs with Fixed Start Times on Related Machines. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2012 2012. Lecture Notes in Computer Science, vol 7408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32512-0_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-32512-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32511-3
Online ISBN: 978-3-642-32512-0
eBook Packages: Computer ScienceComputer Science (R0)