Computer Science - Research and Development

, Volume 27, Issue 3, pp 189–196 | Cite as

Probabilistic alternatives for competitive analysis

Special Issue Paper

Abstract

In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: It sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior, or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.

Keywords

Probabilistic analysis Online optimization Expected competitive ratio Stochastic dominance 

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References

  1. 1.
    Albers S, Favrholdt LM, Giel O (2005) On paging with locality of reference. J Comput Syst Sci 70(2):145–175 MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Anderson EJ, Potts CN (2004) On-line scheduling of a single machine to minimize total weighted completion time. Math Oper Res 29:686–697 MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Angelopoulos S, Schweitzer P (2009) Paging and list update under bijective analysis. In: Proceedings of the 20th ACM-SIAM symposium on discrete algorithms, pp 1136–1145 Google Scholar
  4. 4.
    Angelopoulos S, Dorrigiv R, López-Ortiz A (2007) On the separation and equivalence of paging strategies. In: Proceedings of the 18th ACM-SIAM symposium on discrete algorithms, pp 229–237 Google Scholar
  5. 5.
    Banderier C, Beier R, Mehlhorn K (2003) Smoothed analysis of three combinatorial problems. In: Proceedings of the 28th international symposium on mathematical foundations of computer science. Lecture notes in computer science, vol 2747. Springer, Berlin, pp 198–207 Google Scholar
  6. 6.
    Becchetti L (2004) Modeling locality: a probabilistic analysis of LRU and FWF. In: Proceedings of the 12th European symp on algorithms (ESA), pp 98–109 Google Scholar
  7. 7.
    Becchetti L, Leonardi S (2004) Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. J ACM 51:517–539 MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Becchetti L, Leonardi S, Marchetti-Spaccamela A, Schäfer G, Vredeveld T (2006) Average case and smoothed competitive analysis for the multi-level feedback algorithm. Math Oper Res 31(1):85–108 MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Beier R, Czumaj A, Krysta P, Vöcking B (2004) Computing equilibria for congestion games with (im)perfect information. In: Proceedings of the 15th annual ACM-SIAM symposium on discrete algorithms, pp 739–748 Google Scholar
  10. 10.
    Bentley JL, Johnson DS, Leighton FT, McGeoch CC, McGeoch LA (1984) Some unexpected expected behavior results for bin packing. In: Proceedings of the 16th annual ACM symposium on theory of computing, pp 279–288 Google Scholar
  11. 11.
    Borodin A, Irani S, Raghavan P, Schieber B (1995) Competitive paging with locality of reference. J Comput Syst Sci 50(2):244–258 MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Borodin A, Linial N, Saks ME (1992) An optimal on-line algorithm for metrical task systems. J ACM 39(4):745–763 MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Chandra B (1992) Does randomization help in on-line bin packing? Inf Process Lett 43(1):15–19 CrossRefMATHGoogle Scholar
  14. 14.
    Coffman EG Jr, Gilbert EN (1985) On the expected relative performance of list scheduling. Oper Res 33(3):548–561 MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Coffman EG Jr, So K, Hofri M, Yao AC (1980) A stochastic model of bin-packing. Inf Control 44:105–115 MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Coffman EG Jr, Garey MR, Johnson DS, (1997) Approximation algorithms for bin packing: a survey. In: Hochbaum DS (ed) Approximation algorithms for NP-hard problems. PWS, Boston Google Scholar
  17. 17.
    Coffman EG Jr, Courcoubetis C, Garey MR, Johnson DS, Shor PW, Weber RR, Yannakakis M (2002) Perfect packing theorems and the average-case behavior of optimal and online bin packing. SIAM Rev 44(1):95–108 MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Correa J, Wagner M (2009) LP-based online scheduling: from single machine to parallel machines. Math Program 119(1):109–136 MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Csirik J, Johnson DS (2001) Bounded space on-line bin packing: best is better than first. Algorithmica 11:115–138 MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fiat A, Karp RM, Luby M, McGeoch LA, Sleator DD, Young NE (1991) Competitive paging algorithms. J Algorithms 12:685–699 CrossRefMATHGoogle Scholar
  21. 21.
    Franaszek PA, Wagner TJ (1974) Some distribution-free aspects of paging algorithm performance. J ACM 21(1):31–39 MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Graham RL (1966) Bounds for certain multiprocessor anomalies. Bell Syst Tech J 45:1563–1581 Google Scholar
  23. 23.
    Hiller B (2009) Online optimization: probabilistic analysis and algorithm engineering. PhD thesis, TU Berlin Google Scholar
  24. 24.
    Hiller B, Vredeveld T (2008) On the optimality of least recently used. ZIB-Report 08-39, Zuse Institute Berlin Google Scholar
  25. 25.
    Hiller B, Vredeveld T (2008) Probabilistic analysis of online bin coloring algorithms via stochastic comparison. In: Proceedings of the 16th annual European symposium on algorithms. Lecture notes in computer science, vol 5193. Springer, Berlin, pp 528–539 Google Scholar
  26. 26.
    Hoogeveen H, Vestjens APA (1996) Optimal on-line algorithms for single-machine scheduling. In: Cunningham WH, McCormick ST, Queyranne M (eds) Proceedings of the 5th conference on integer programming and combinatorial optimization IPCO. Lecture notes in computer science, vol 1084. Springer, Berlin, pp 404–414 Google Scholar
  27. 27.
    Johnson DS (1974) Fast algorithms for bin packing. J Comput Syst Sci 8(8):272–314 CrossRefMATHGoogle Scholar
  28. 28.
    Johnson DS, Demers A, Ullman JD, Garey MR, Graham RL (1974) Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J Comput 3(4):299–325 MathSciNetCrossRefGoogle Scholar
  29. 29.
    Kalyanasundaram B, Pruhs K (2000) Speed is as powerful as clairvoyance. J ACM 47(4):617–643 MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Karlin AR, Manasse MS, Rudolph L, Sleator DD (1988) Competitive snoopy caching. Algorithmica 3:70–119 MathSciNetCrossRefGoogle Scholar
  31. 31.
    Karlin AR, Phillips SJ, Raghavan P (2000) Markov paging. SIAM J Comput 30(2):906–922 MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Kawaguchi T, Kyan S (1986) Worst case bound of an LRF schedule for the mean weighted flow-time problem. SIAM J Comput 15:1119–1129 MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Koutsoupias E, Papadimitriou C (1994) Beyond competitive analysis. In: Proceedings of the 35th annual IEEE symposium on foundations of computer science, pp 394–400 Google Scholar
  34. 34.
    Krumke SO, de Paepe WE, Stougie L, Rambau J (2001) Online bin coloring. In: auf der Heide FM (ed) Proceedings of the 9th annual European symposium on algorithms. Lecture notes in computer science, vol 2161, pp 74–84 Google Scholar
  35. 35.
    Lee CC, Lee DT (1985) A simple online bin-packing algorithm. J ACM 32(3):562–572 CrossRefMATHGoogle Scholar
  36. 36.
    McGeoch LA, Sleator DD (1991) A strongly competitive randomized paging algorithm. Algorithmica 6:816–825 MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Möhring RH, Schulz AS, Uetz M (1999) Approximation in stochastic scheduling: the power of LP-based priority policies. J ACM 46:924–942 MathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Motwani R, Phillips S, Torng E (1994) Non-clairvoyant scheduling. Theor Comput Sci 130:17–47 MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    Panagiotou K, Souza A (2006) On adequate performance measures for paging. In: STOC ’06: Proceedings of the 38th annual ACM symposium on theory of computing, pp 487–496 CrossRefGoogle Scholar
  40. 40.
    Pruhs K, Sgall J, Torng E (2004) Online scheduling. In: Leung J (ed) Handbook of scheduling: algorithms, models, and performance analysis. CRC Press, Boca Raton Google Scholar
  41. 41.
    Richey MB (1991) Improved bounds for harmonic-based bin packing algorithms. Discrete Appl Math 34(1–3):203–227 MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Scharbrodt M, Schickinger T, Steger A (2006) A new average case analysis for completion time scheduling. J. ACM 121–146 Google Scholar
  43. 43.
    Schrage L (1968) A proof of the optimality of the shortest remaining processing time discipline. Oper Res 16:687–690 CrossRefMATHGoogle Scholar
  44. 44.
    Seiden S (2000) A guessing game and randomized online algorithms. In: Proceedings of the 32nd ACM symposium on theory of computing, pp 592–601 Google Scholar
  45. 45.
    Shor PW (1986) The average-case analysis of some on-line algorithms for bin packing. Combinatorica 6(2):179–200 MathSciNetCrossRefMATHGoogle Scholar
  46. 46.
    Sleator DD, Tarjan RE (1985) Amortized efficiency of list update and paging rules. Commun ACM 28(2):202–208 MathSciNetCrossRefGoogle Scholar
  47. 47.
    Souza A (2010) Adversarial models in paging—bridging the gap between theory and practice. Comput Sci Res Dev, this issue Google Scholar
  48. 48.
    Souza A, Steger A (2006) The expected competitive ratio for weighted completion time scheduling. Theory Comput Syst 39:121–136 MathSciNetCrossRefMATHGoogle Scholar
  49. 49.
    Spielman DA, Teng SH (2004) Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. J ACM 51:385–463 MathSciNetCrossRefMATHGoogle Scholar
  50. 50.
    Torng E (1998) A unified analysis of paging and caching. Algorithmica 20(1):175–200 MathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    van Vliet A (1996) On the asymptotic worst case behavior of harmonic fit. J Algorithms 20(1):113–136 MathSciNetCrossRefMATHGoogle Scholar
  52. 52.
    Vestjens APA (1997) On-line machine scheduling. PhD thesis, Eindhoven University of Technology, Netherlands Google Scholar
  53. 53.
    Vredeveld T (2010) Stochastic online scheduling. Comput Sci Res Dev, this issue Google Scholar
  54. 54.
    Yao AC (1980) New algorithms for bin packing. J ACM 27(2):207–227 CrossRefMATHGoogle Scholar
  55. 55.
    Young NE (1994) The k-server dual and loose competitiveness for paging. Algorithmica 11(6):525–541 MathSciNetCrossRefGoogle Scholar
  56. 56.
    Young NE (2000) On-line paging against adversarially biased random inputs. J Algorithms 37(1):218–235 MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Department of Quantitative EconomicsMaastricht UniversityMaastrichtThe Netherlands

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