Abstract
We consider the online scheduling of unit length jobs with two models of commitment. In immediate notification, the acceptance of a job must be decided as soon as it is released. In immediate decision, the actual time slot allocated to the job must also be fixed at the job’s arrival as well. Failure to honour a commitment will result in a penalty. The non-commitment version has been extensively studied. In this paper we give algorithms and lower bounds for the two models of commitment. For immediate decision, we give an O(m(1 + ρ)1/m)-competitive algorithm where m is the number of machines and ρ is the penalty factor, and when m is large we give an O(log(1 + ρ)) upper bound. This is matched by a lower bound of Ω(logρ) on the competitive ratio. For immediate notification we give a lower bound of Ω(logρ/loglogρ). We also give some better bounds when m = 1 or when ρ is small. Finally we give considerations to the case of separate arrival and start times.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Babaioff, M., Hartline, J.D., Kleinberg, R.D.: Selling ad campaigns: online algorithms with cancellations. In: Proc. 10th ACM Conference on Electronic Commerce, pp. 61–70 (2009)
Bunde, D.P., Goldwasser, M.H.: Dispatching equal-length jobs to parallel machines to maximize throughput. In: Kaplan, H. (ed.) SWAT 2010. LNCS, vol. 6139, pp. 346–358. Springer, Heidelberg (2010)
Chen, S., Tong, L., He, T.: Optimal deadline scheduling with commitment. In: 49th Annual Allerton Conference on Communication, Control and Computing, pp. 111–118 (2011)
Chin, F.Y.L., Chrobak, M., Fung, S.P.Y., Jawor, W., Sgall, J., Tichý, T.: Online competitive algorithms for maximizing weighted throughput of unit jobs. Journal of Discrete Algorithms 4(2), 255–276 (2006)
Chin, F.Y.L., Fung, S.P.Y.: Online scheduling with partial job values: Does timesharing or randomization help? Algorithmica 37(3), 149–164 (2003)
Cole, R., Dobzinski, S., Fleischer, L.K.: Prompt mechanisms for online auctions. In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 170–181. Springer, Heidelberg (2008)
Constantin, F., Feldman, J., Muthukrishnan, S., Pal, M.: An online mechanism for ad slot reservations with cancellations. In: Proc. 20th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1265–1274 (2009)
Ding, J., Ebenlendr, T., Sgall, J., Zhang, G.: Online scheduling of equal-length jobs on parallel machines. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 427–438. Springer, Heidelberg (2007)
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)
Ebenlendr, T., Sgall, J.: A lower bound for scheduling of unit jobs with immediate decision on parallel machines. In: Bampis, E., Skutella, M. (eds.) WAOA 2008. LNCS, vol. 5426, pp. 43–52. Springer, Heidelberg (2009)
Englert, M., Westermann, M.: Considering suppressed packets improves buffer management in QoS switches. In: Proc. 18th ACM-SIAM Symposium on Discrete Algorithms, pp. 209–218 (2007)
Fung, S.P.Y.: Online preemptive scheduling with immediate decision or notification and penalties. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 389–398. Springer, Heidelberg (2010)
Goldwasser, M.H.: A survey of buffer management policies for packet switches. SIGACT News 45(1), 100–128 (2010)
Goldwasser, M.H., Kerbikov, B.: Admission control with immediate notification. Journal of Scheduling 6, 269–285 (2003)
Hajek, B.: On the competitiveness of on-line scheduling of unit-length packets with hard deadlines in slotted time. In: Proc. Conference on Information Sciences and Systems, pp. 434–438 (2001)
Kaminsky, P., Hochbaum, D.: Due date quotation models and algorithms. In: Leung, J.Y.-T., Henderson, J.H. (eds.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis, ch. 20. Chapman and Hall/CRC (2004)
Keskinocak, P., Ravi, R., Tayur, S.: Scheduling and reliable lead-time quotation for orders with availability intervals and lead-time sensitive revenues. Management Science 47(2), 264–279 (2001)
Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. In: Proc. 33th ACM Symposium on Theory of Computing, pp. 520–529 (2001)
Pruhs, K., Sgall, J., Torng, E.: Online Scheduling. In: Leung, J.Y.-T., Henderson, J.H. (eds.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis, ch. 15. Chapman and Hall/CRC (2004)
Zhu, A.: Analysis of queueing policies in QoS switches. Journal of Algorithms 53, 137–168 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 IFIP International Federation for Information Processing
About this paper
Cite this paper
Fung, S.P.Y. (2014). Online Scheduling of Unit Length Jobs with Commitment and Penalties. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds) Theoretical Computer Science. TCS 2014. Lecture Notes in Computer Science, vol 8705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44602-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-44602-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44601-0
Online ISBN: 978-3-662-44602-7
eBook Packages: Computer ScienceComputer Science (R0)