Journal of Combinatorial Optimization

, Volume 36, Issue 4, pp 1168–1194 | Cite as

Cost-efficient scheduling on machines from the cloud

  • Alexander MäckerEmail author
  • Manuel Malatyali
  • Friedhelm Meyer auf der Heide
  • Sören Riechers


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 deadlines and machine-type dependent sizes. The objective is to rent machines and schedule jobs so as to meet all deadlines while minimizing the rental cost. As we observe the slack of jobs to have a fundamental influence on the competitiveness, we parameterize instances 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 online algorithm for \(\beta = (1+\varepsilon )s\) with Open image in new window , where s denotes the largest setup time. Its competitiveness only depends on \(\varepsilon \) and the cost ratio of the machine types and is proven to be optimal up to a factor of Open image in new window .


Scheduling Setup times Cloud Competitiveness 


  1. Abshoff S, Markarian C, Meyer auf der Heide F (2014) Randomized online algorithms for set cover leasing problems. In: Zhang Z, Wu L, Xu W, Du DZ (eds) COCOA 2014, LNCS, vol 8881. Springer, Berlin, pp 25–34Google Scholar
  2. Amazon EC2. Accessed Nov 2017
  3. Anthony MB, Gupta A (2007) Infrastructure leasing problems. In: Fischetti M, Williamson DP (eds) IPCO 2007, LNCS, vol 4513. Springer, Berlin, pp 424–438Google Scholar
  4. Azar Y, Ben-Aroya N, Devanur N-R, Jain N (2013) Cloud scheduling with setup cost. In: Proceedings of the 25th ACM symposium on parallelism in algorithms and architectures (SPAA’13). ACM, pp 298–304Google Scholar
  5. Bender MA, Bunde DP, Leung VJ, McCauley S, Phillips CA (2013) Efficient scheduling to minimize calibrations. In: Proceedings of the 25th ACM symposium on parallelism in algorithms and architectures (SPAA’13). ACM, pp 280–287Google Scholar
  6. Chuzhoy J, Guha S, Khanna S, Naor J (2004) Machine minimization for scheduling jobs with interval constraints. In: Proceedings of the 45th symposium on foundations of computer science (FOCS’04). IEEE, pp 81–90Google Scholar
  7. Devanur NR, Makarychev K, Panigrahi D, Yaroslavtsev G (2014) Online algorithms for machine minimization. CoRR. arXiv:1403.0486
  8. Fineman TJ, Sheridan B (2015) Scheduling non-unit jobs to minimize calibrations. In: Proceedings of the 27th ACM symposium on parallelism in algorithms and architectures (SPAA’15). ACM, pp 161–170Google Scholar
  9. Google Cloud. Accessed Nov 2017
  10. Kling P, Meyer auf der Heide F, Pietrzyk P (2012) An algorithm for online facility leasing. In: Even G, Halldórsson MM (eds) SIROCCO 2012, LNCS, vol 7355. Springer, Berlin, pp 61–72CrossRefGoogle Scholar
  11. Lee G, Chun B-G, Katz RH (2001) Heterogeneity-aware resource allocation and scheduling in the cloud. In: Proceedings of the 3rd USENIX workshop on hot topics in cloud computing (HotCloud’11). USENIXGoogle Scholar
  12. Li S, Mäcker A, Markarian C, Meyer auf der Heide F, Riechers S (2015) Towards flexible demands in online leasing problems. In: Proceedings of the 21st international conference on computing and combinatorics (COCOON’15). Springer, Berlin, pp 277–288zbMATHGoogle Scholar
  13. Malik S, Huet F (2011) Virtual cloud: rent out the rented resources. In: Proceedings of the 2011 international conference on internet technology and secured transactions (ICITST’11). IEEE, pp 536–541Google Scholar
  14. Mao M, Humphrey M (2012) A performance study on the VM startup time in the cloud. In: Proceedings of the 2012 IEEE 5th international conference on cloud computing (ICCC’12). IEEE, pp 423–430Google Scholar
  15. Mao M, Li J, Humphrey M (2010) Cloud auto-scaling with deadline and budget constraints. In: Proceedings of the 2010 11th IEEE/ACM international conference on grid computing (GRID’10). IEEE, pp 41–48Google Scholar
  16. Meyerson A (2005) The parking permit problem. In: Proceedings of the 46th annual symposium on foundations of computer science (FOCS’05). IEEE, pp 274–282Google Scholar
  17. Raghavan P, Thompson CD (1987) Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7(4):365–374MathSciNetCrossRefGoogle Scholar
  18. Saha B (2013) Renting a cloud. In: Proceedings of the annual conference on foundations of software technology and theoretical computer science (FSTTCS’13). LIPIcs, pp 437–448Google Scholar
  19. Sgall J (2014) Online bin packing: old algorithms and new results. In: Beckmann A, Csuhaj-Varjú E, Meer K (eds) CiE 2014, LNCS, vol 8493. Springer, Berlin, pp 362–372Google Scholar
  20. Yu G, Zhang G (2009) Scheduling with a minimum number of machines. Oper Res Lett 37(2):97–101MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Alexander Mäcker
    • 1
    Email author
  • Manuel Malatyali
    • 1
  • Friedhelm Meyer auf der Heide
    • 1
  • Sören Riechers
    • 1
  1. 1.Paderborn UniversityPaderbornGermany

Personalised recommendations