Journal of Scheduling

, Volume 18, Issue 4, pp 393–410 | Cite as

Improved upper bounds for online malleable job scheduling

  • Nathaniel Kell
  • Jessen Havill


In this paper, we study online algorithms that schedule malleable jobs, i.e., jobs that can be parallelized on any subset of the available \(m\) identical machines. We study a model that accounts for the tradeoff between multiprocessor speedup and overhead time, namely, if job \(j\) has processing requirement \(p_j\) and is assigned to run on \(k_j\) machines, then \(j\)’s execution time becomes \(p_j/k_j + (k_j -1)c\), where \(c\) is a constant parameter to the problem. For \(m=2\), we present an online algorithm OCS that has a strong competitive ratio of 3/2, matching a previously established lower bound. We also present an online algorithm ASYM2 that is asymptotically \(((4-\epsilon )/(3-\epsilon ))\)-competitive when \(m=2\), where \(0 < \epsilon \le 2\) is a parameter to the algorithm, improving upon an existing asymptotically (3/2)-competitive algorithm. Finally, we present an online algorithm OTO that is strongly \(2\)-competitive when \(m = 3\), improving upon the previous best upper bound of \(9/4\).


Online algorithms Scheduling Parallel jobs Identical machines Overhead time 


  1. Baker, B. S., Coffman, E. G, Jr, & Rivest, R. L. (1980). Orthogonal packings in two dimensions. SIAM Journal on Computing, 9(4), 846–855.CrossRefGoogle Scholar
  2. Bartal, Y., Fiat, A., Karloff, H. J., & Vohra, R. (1995). New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences, 51(3), 359–366.CrossRefGoogle Scholar
  3. Carroll, T. E., & Grosu, D. (2010). Incentive compatible online scheduling of malleable parallel jobs with individual deadlines. In Proceedings of ICPP (pp. 516–524). IEEE Computer Society.Google Scholar
  4. Chen, B., van Vliet, A., & Woeginger, G. J. (1994). New lower and upper bounds for on-line scheduling. Operations Research Letters, 16(4), 221–230.CrossRefGoogle Scholar
  5. Coffman, E. G, Jr, Garey, M. R., Johnson, D. S., & Tarjan, R. E. (1980). Performance bounds for level-oriented two-dimensional packing algorithms. SIAM Journal on Computing, 9(4), 808–826.CrossRefGoogle Scholar
  6. Du, J., & Leung, J. (1989). Complexity of scheduling parallel task systems. SIAM Journal on Discrete Mathematics, 2(4), 473–487.CrossRefGoogle Scholar
  7. Dutton, R. A., & Mao, W. (2007). Online scheduling of malleable parallel jobs. In Proceedings of ICPDCS (pp. 1–6). IASTED.Google Scholar
  8. Dutton, R. A., Mao, W., Chen, J., & Watson, W. A. III (2008). Parallel job scheduling with overhead: A benchmark study. In Proceedings of NAS (pp. 326–333). IEEE Computer Society.Google Scholar
  9. Faigle, U., Kern, W., & Turán, G. (1989). On the performance of on-line algorithms for partition problems. Acta Cybernetica, 9(2), 107–119.Google Scholar
  10. Garey, M. R., & Graham, R. L. (1975). Bounds for multiprocessor scheduling with resource constraints. SIAM Journal on Computing, 4(2), 187–200.CrossRefGoogle Scholar
  11. Graham, R. L. (1969). Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17(2), 416–429.CrossRefGoogle Scholar
  12. Guo, S., & Kang, L. (2010). Online scheduling of malleable parallel jobs with setup times on two identical machines. European Journal of Operational Research, 206(3), 555–561.CrossRefGoogle Scholar
  13. Harren, R., & Kern, W. (2011). Improved lower bound for online strip packing—(extended abstract). In Proceedings of WAOA, LNCS (Vol. 7164, pp. 211–218). Springer.Google Scholar
  14. Havill, J. T., & Mao, W. (2008). Competitive online scheduling of perfectly malleable jobs with setup times. European Journal of Operational Research, 187(3), 1126–1142.CrossRefGoogle Scholar
  15. Havill, J. T. (2010). Online malleable job scheduling for m\(\le \)3. Information Processing Letters, 111(1), 31–35.CrossRefGoogle Scholar
  16. Hurink, J. L., & Paulus, J. J. (2011). Improved online algorithms for parallel job scheduling and strip packing. Theoretical Computer Science, 412(7), 583–593.CrossRefGoogle Scholar
  17. Johannes, B. (2006). Scheduling parallel jobs to minimize the makespan. Journal of Scheduling, 9(5), 433–452.CrossRefGoogle Scholar
  18. Karloff, H. J., Suri, S., & Vassilvitskii, S. (2010). A model of computation for mapreduce. In Proceedings of SODA (pp. 938–948). SIAM.Google Scholar
  19. Moseley, B., Dasgupta, A., Kumar, R., & Sarlós, T. (2011). On scheduling in map-reduce and flow-shops. In Proceedings of SPAA (pp. 289–298). ACM.Google Scholar
  20. Nagarajan, V., Wolf, J. L., Balmin, A., & Hildrum, K. (2013). Flowflex: Malleable scheduling for flows of mapreduce jobs. In Proceedings of Middleware, LNCS (Vol. 8275, pp. 103–122). Springer.Google Scholar
  21. Naroska, E., & Schwiegelshohn, U. (2002). On an on-line scheduling problem for parallel jobs. Information Processing Letters, 81(6), 297–304.CrossRefGoogle Scholar
  22. Schwiegelshohn, U., Ludwig, W., Wolf, J. L., Turek, J., & Yu, P. S. (1998). Smart smart bounds for weighted response time scheduling. SIAM Journal on Computing, 28(1), 237–253.Google Scholar
  23. Sgall, J. (1994). On-line scheduling of parallel jobs. In Proceedings of MFCS, LNCS (vol. 841, pp. 159–176). Springer.Google Scholar
  24. Sleator, D. D. (1980). A 2.5 times optimal algorithm for packing in two dimensions. Information Processing Letters, 10(1), 37–40.CrossRefGoogle Scholar
  25. Turek, J., Wolf, J. L., & Yu, P. S. (1992). Approximate algorithms scheduling parallelizable tasks. In Proceedings of SPAA (pp. 323–332). ACM.Google Scholar
  26. Ye, D., & Zhang, G. (2007). On-line scheduling of parallel jobs in a list. Journal of Scheduling, 10(6), 407–413.CrossRefGoogle Scholar
  27. Ye, D., Han, X., & Zhang, G. (2009). A note on online strip packing. Journal of Combinatorial Optimization, 17(4), 417–423.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Department of Mathematics and Computer ScienceDenison UniversityGranvilleUSA

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