Journal of Scheduling

, Volume 14, Issue 1, pp 89–101 | Cite as

Competitive ratio of List Scheduling on uniform machines and randomized heuristics



We study online scheduling on m uniform machines, where m−1 of them have a reference speed 1 and the last one a speed s with 0≤s≤1. The competitive ratio of the well-known List Scheduling (LS) algorithm is determined. For some values of s and m=3, LS is proven to be the best deterministic algorithm. We describe a randomized heuristic for m machines. Finally, for the case m=3, we develop and analyze the competitive ratio of a randomized algorithm which outperforms LS for any s.


Analysis of algorithms Online algorithms Competitive ratio Randomized scheduling 


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  1. Bartal, Y., Fiat, A., Karloff, H., & Vohra, R. (1995). New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences, 51(3), 359–366. CrossRefGoogle Scholar
  2. Borodin, A., Irani, S., Raghavan, P., & Schieber, B. (1995). Competitive paging with locality of reference. Journal of Computer and System Sciences, 50(2), 244–258. CrossRefGoogle Scholar
  3. Cheng, T. C. E., Ng, C. T., & Kotov, V. (2006). A new algorithm for online uniform-machine scheduling to minimize the makespan. Information Processing Letters, 99(3), 102–105. CrossRefGoogle Scholar
  4. Cho, Y., & Sahni, S. (1980). Bounds for list schedules on uniform processors. SIAM Journal on Computing, 9(1), 91–103. CrossRefGoogle Scholar
  5. Epstein, L., Noga, J., Seiden, S., Sgall, J., & Woeginger, G. (2001). Randomized on-line scheduling on two uniform machines. Journal of Scheduling, 4(2), 71–92. CrossRefGoogle Scholar
  6. Hochbaum, D. S. (1997). Approximation algorithms for NP-hard problems. Boston: PWS Publishing Company. Google Scholar
  7. Kokash, N. (2004). An efficient heuristic for on-line scheduling in system with one fast machine. Master Thesis. Google Scholar
  8. Li, R., & Shi, L. (1998). An on-line algorithm for some uniform processor scheduling. SIAM Journal on Computing, 27(2), 414–422. CrossRefGoogle Scholar
  9. Seiden, S. S. (2000). Randomized online multiprocessor scheduling. Algorithmica, 28(2), 173–216. CrossRefGoogle Scholar
  10. Sgall, J. (1994). On-line scheduling on parallel machines. Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica pura ed applicataUniversità degli Studi di PadovaPadovaItaly
  2. 2.ROSO/IMAEPFLLausanneSwitzerland

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