Abstract
We consider the non-preemptive scheduling of two identical machines for jobs with equal processing times yet arbitrary release dates and deadlines. Our objective is to maximize the number of jobs completed by their deadlines. Using standard nomenclature, this problem is denoted as \({\it P}2 \mid {p_j = p,r_j} \mid {\sum \overline{U}_j}\). The problem is known to be polynomially solvable in an offline setting.
In an online variant of the problem, a job’s existence and parameters are revealed to the scheduler only upon that job’s release date. We present an online, deterministic algorithm for the problem and prove that it is \(\frac{3}{2}\)-competitive. A simple lower bound shows that this is the optimal deterministic competitiveness.
This material is based upon work supported by the National Science Foundation under Grant No. CCR-0417368.
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.G.: Ten notes on equal-processing-time scheduling. 4OR: Quarterly J. Belgian, French and Italian Operations Research Societies 2(2), 111–127 (2004)
Baruah, S.K., Haritsa, J.R., Sharma, N.: On-line scheduling to maximize task completions. J. Combin. Math. and Combin. Computing 39, 65–78 (2001)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, New York (1998)
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., Parwatikar, J., Suri, S.: On-line scheduling with hard deadlines. J. Algorithms 34(2), 370–389 (2000)
Goldwasser, M.H.: Patience is a virtue: The effect of slack on competitiveness for admission control. J. Scheduling 6(2), 183–211 (2003)
Goldwasser, M.H., Kerbikov, B.: Admission control with immediate notification. J. Scheduling 6(3), 269–285 (2003)
Jackson, J.R.: Scheduling a production line to minimize maximum tardiness. Research Report 43, Management Science Research Project, University of California, Los Angeles (January 1955)
Simons, B.B.: Multiprocessor scheduling of unit length jobs with arbitrary release times and deadlines. SIAM J. Comput. 12, 294–299 (1983)
Simons, B.B., Warmuth, M.K.: A fast algorithm for multiprocessor scheduling of unit-length jobs. SIAM J. Comput. 18(4), 690–710 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goldwasser, M.H., Pedigo, M. (2006). Online, Non-preemptive Scheduling of Equal-Length Jobs on Two Identical Machines. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_13
Download citation
DOI: https://doi.org/10.1007/11785293_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35753-7
Online ISBN: 978-3-540-35755-1
eBook Packages: Computer ScienceComputer Science (R0)