Abstract
We study on-line scheduling of equal-length jobs on parallel machines. Our main result is an algorithm with competitive ratio decreasing to e/(e − 1) ≈ 1.58 as the number of machine increases. For m ≥ 3, this is the first algorithm better than 2-competitive greedy algorithm.
Our algorithm has an additional property called immediate decision: at each time, it is immediately decided for each newly released job if it will be scheduled, and if so, then also the time interval and machine where it is scheduled is fixed and cannot be changed later. We show that for two machines, no deterministic algorithm with immediate decision is better than 1.8-competitive; this lower bound shows that our algorithm is optimal for m = 2 in this restricted model. We give some additional lower bounds for algorithms with immediate decision.
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
Baptiste, P., Brucker, P., Knust, S., Timkovsky, V.: Ten notes on equal-execution-time scheduling. 4OR 2, 111–127 (2004)
Baruah, S.K., Haritsa, J., Sharma, N.: On-line scheduling to maximize task completions. J. Comb. Math. Comb. Comput. 39, 65–78 (2001) (A preliminary version appeared. Proc. 15th Real-Time Systems Symp., IEEE, pp. 228–236 (1994) )
Chrobak, M., Jawor, W., Sgall, J., Tichý, T.: Online scheduling of equal-length jobs: Randomization and restarts help. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 358–370. Springer, Heidelberg (2004)
Ding, J., Zhang, G.: Online scheduling with hard deadlines on parallel machines. In: Cheng, S.-W., Poon, C.K. (eds.) AAIM 2006. LNCS, vol. 4041, pp. 32–42. Springer, Heidelberg (2006)
Goldman, S.A., Parwatikar, J., Suri, S.: Online scheduling with hard deadlines. J. Algorithms 34, 370–389 (2000)
Goldwasser, M.H., Kerbikov, B.: Admission control with immediate notification. J. Sched. 6, 269–285 (2003)
Goldwasser, M.H., Pedigo, M.: Online, non-preemptive scheduling of equal-length jobs on two identical machines. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 113–123. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ding, J., Ebenlendr, T., Sgall, J., Zhang, G. (2007). Online Scheduling of Equal-Length Jobs on Parallel Machines. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_39
Download citation
DOI: https://doi.org/10.1007/978-3-540-75520-3_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75519-7
Online ISBN: 978-3-540-75520-3
eBook Packages: Computer ScienceComputer Science (R0)