Abstract
We consider a scheduling problem where machines need to be rented from the cloud in order to process jobs. There are two types of machines available which can be rented for machine-type dependent prices and for arbitrary durations. However, a machine-type dependent setup time is required before a machine is available for processing. Jobs arrive online over time, have machine-type dependent sizes and have individual deadlines. The objective is to rent machines and schedule jobs so as to meet all deadlines while minimizing the rental cost.
Since we observe the slack of jobs to have a fundamental influence on the competitiveness, we study the model when instances are parameterized by their (minimum) slack. An instance is called to have a slack of \(\beta \) if, for all jobs, the difference between the job’s release time and the latest point in time at which it needs to be started is at least \(\beta \). While for \(\beta < s\) no finite competitiveness is possible, our main result is an 
-competitive online algorithm for \(\beta = (1+\varepsilon )s\) with 
, where s and c denotes the largest setup time and the cost ratio of the machine-types, respectively. It is complemented by a lower bound of 
.
This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901).
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References
Abshoff, S., Markarian, C., Meyer auf der Heide, F.: Randomized online algorithms for set cover leasing problems. In: Zhang, Z., Wu, L., Xu, W., Du, D.-Z. (eds.) COCOA 2014. LNCS, vol. 8881, pp. 25–34. Springer, Heidelberg (2014). doi:10.1007/978-3-319-12691-3_3
Amazon EC2. https://aws.amazon.com/ec2/
Anthony, B.M., Gupta, A.: Infrastructure leasing problems. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, pp. 424–438. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72792-7_32
Azar, Y., Ben-Aroya, N., Devanur, N.-R., Jain, N.: Cloud scheduling with setup cost. In: Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2013), pp. 298–304. ACM (2013)
Bender, M.A., Bunde, D.P., Leung, V.J., McCauley, S., Phillips, C.A.: Efficient scheduling to minimize calibrations. In: Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2013), pp. 280–287. ACM (2013)
Chuzhoy, J., Guha, S., Khanna, S., Naor, J.: Machine minimization for scheduling jobs with interval constraints. In: Proceedings of the 45th Symposium on Foundations of Computer Science (FOCS 2004), pp. 81–90. IEEE (2004)
Devanur, N.R., Makarychev K., Panigrahi, D., Yaroslavtsev, G.: Online Algorithms for Machine Minimization. CoRR (2014). 1403.0486
Fineman, T.J., Sheridan, B.: Scheduling non-unit jobs to minimize calibrations. In: Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2015), pp. 161–170. ACM (2015)
Google Cloud. https://cloud.google.com/
Kling, P., Meyer auf der Heide, F., Pietrzyk, P.: An algorithm for online facility leasing. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 61–72. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31104-8_6
Lee, G., Chun, B.-G., Katz, R.H.: Heterogeneity-aware resource allocation and scheduling in the cloud. In: Proceedings of the 3rd USENIX Workshop on Hot Topics in Cloud Computing (HotCloud 2011). USENIX (2001)
Mao, M., Humphrey, M.: A performance study on the VM startup time in the cloud. In: Proceedings of the 2012 IEEE 5th International Conference on Cloud Computing (ICCC 2012), pp. 423–430. IEEE (2012)
Mao, M., Li, J., Humphrey, M.: Cloud auto-scaling with deadline and budget constraints. In: Proceedings of the 2010 11th IEEE/ACM International Conference on Grid Computing (GRID 2010), pp. 41–48. IEEE (2010)
Mäcker, A., Malatyali, M., Meyer auf der Heide, F., Riechers, S.: Cost-Efficient Scheduling on Machines from the Cloud. CoRR (2016). 1609.01184
Meyerson, A.: The parking permit problem. In: Proceedings of the 46th Annual Symposium on Foundations of Computer Science (FOCS 2005), pp. 274–282. IEEE (2005)
Raghavan, P., Thompson, C.D.: Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7(4), 365–374 (1987)
Saha, B.: Renting a cloud. In: Proceedings of the Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), pp. 437–448. LIPIcs (2013)
Sgall, J.: Online bin packing: old algorithms and new results. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds.) CiE 2014. LNCS, vol. 8493, pp. 362–372. Springer, Heidelberg (2014). doi:10.1007/978-3-319-08019-2_38
Yu, G., Zhang, G.: Scheduling with a minimum number of machines. Oper. Res. Lett. 37(2), 97–101 (2009)
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Mäcker, A., Malatyali, M., der Heide, F.M.a., Riechers, S. (2016). Cost-Efficient Scheduling on Machines from the Cloud. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_42
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