Journal of Combinatorial Optimization

, Volume 12, Issue 4, pp 363–386 | Cite as

Separating online scheduling algorithms with the relative worst order ratio

  • Leah Epstein
  • Lene M. Favrholdt
  • Jens S. Kohrt


The relative worst order ratio is a measure for the quality of online algorithms. Unlike the competitive ratio, it compares algorithms directly without involving an optimal offline algorithm. The measure has been successfully applied to problems like paging and bin packing. In this paper, we apply it to machine scheduling. We show that for preemptive scheduling, the measure separates multiple pairs of algorithms which have the same competitive ratios; with the relative worst order ratio, the algorithm which is “intuitively better” is also provably better. Moreover, we show one such example for non-preemptive scheduling.


Online algorithms Relative worst order ratio Scheduling 


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  1. Albers S (1999) Better bounds for online scheduling. SIAM J Comput 29(2):459–473MathSciNetCrossRefGoogle Scholar
  2. Bartal Y, Fiat A, Karloff H, Vohra R (1995) New algorithms for an ancient scheduling problem. J Comput Syst Sci 51(3):359–366MathSciNetCrossRefGoogle Scholar
  3. Ben-David S, Borodin A (1994) A new measure for the study of on-line algorithms. Algorithmica 11(1):73–91zbMATHMathSciNetCrossRefGoogle Scholar
  4. Boyar J, Favrholdt LM (2003) The relative worst order ratio for on-line algorithms. In Proc. 5th Italian conf. on algorithms and complexity, vol. 2653 of Lect Notes Comp Sci Springer-Verlag, pp 58–69Google Scholar
  5. Boyar J, Favrholdt LM, Larsen KS (2005) The relative worst order ratio applied to paging. In Proc. 16th Annu. ACM-SIAM symp. discrete algorithms, pp 718–727Google Scholar
  6. Boyar J, Medvedev P (2004) The relative worst order ratio applied to seat reservation. In Proc. of the 9th scand. workshop on algorithm theory, vol. 3111 in Lect Notes Comp Sci pp 90–101Google Scholar
  7. Chen B, van Vliet A, Woeginger GJ (1995) An optimal algorithm for preemptive on-line scheduling. Oper Res Lett 18(3):127–131zbMATHMathSciNetCrossRefGoogle Scholar
  8. Cho Y, Sahni S (1980) Bounds for list schedules on uniform processors. SIAM J Comput 9(1):91–103zbMATHMathSciNetCrossRefGoogle Scholar
  9. Epstein L, Noga J, Seiden SS, Sgall J, Woeginger GJ (2001) Randomized online scheduling on two uniform machines. J Sched 4(2):71–92zbMATHMathSciNetCrossRefGoogle Scholar
  10. Epstein L, Sgall J (2000) A lower bound for on-line scheduling on uniformly related machines. Oper Res Lett 26(1):17–22zbMATHMathSciNetCrossRefGoogle Scholar
  11. Faigle U, Kern W, Turän G (1989) On the performance of on-line algorithms for partition problems. Acta Cybernet 9(2):107–119zbMATHMathSciNetGoogle Scholar
  12. Fleischer R, Wahl M (2000) On-line scheduling revisited. J Sched 3(6):343–353zbMATHMathSciNetCrossRefGoogle Scholar
  13. Galambos G, Woeginger GJ (1993) An on-line scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM J Comput 22(2):349–355zbMATHMathSciNetCrossRefGoogle Scholar
  14. Gonzalez T, Sahni S (1978) Preemptive scheduling of uniform processor systems. J ACM 25(1):92–101zbMATHMathSciNetCrossRefGoogle Scholar
  15. Gormley T, Reingold N, Torng E, Westbrook J (2000) Generating adversaries for request-answer games. In Proc. 11th annu. ACM-SIAM symp. on discrete algorithms, pp 564–565Google Scholar
  16. Graham RL (1966) Bounds for certain multiprocessing anomalies. Bell Systems Techn J 45:1563–1581Google Scholar
  17. Karger DR, Philips SJ, Torng E (1996) A better algorithm for an ancient scheduling problem. J Algorithms 20(2):400–430zbMATHMathSciNetCrossRefGoogle Scholar
  18. Kenyon C (1996) Best-fit bin-packing with random order. In Proc. 7th annu. ACM-SIAM symp. on discrete algorithms, pp 359–364Google Scholar
  19. Kohrt JS (2004) Online algorithms under new assumptions, PhD thesis, Dept Math and Comp Sci, Univ South Den, p. 78.Google Scholar
  20. McNaughton R (1959) Scheduling with deadlines and loss functions. Manag Sci 6(1):1–12zbMATHMathSciNetCrossRefGoogle Scholar
  21. Seiden SS (2001) Preemptive multiprocessor scheduling with rejection. Theoret Comp Sci 262(1–2):437–458zbMATHMathSciNetCrossRefGoogle Scholar
  22. Wen J, Du D (1998) Preemptive on-line scheduling for two uniform processors. Oper Res Lett 23:113–116zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Leah Epstein
    • 1
  • Lene M. Favrholdt
    • 2
  • Jens S. Kohrt
    • 2
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark

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