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Probabilistic alternatives for competitive analysis

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Computer Science - Research and Development

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.

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References

  1. Albers S, Favrholdt LM, Giel O (2005) On paging with locality of reference. J Comput Syst Sci 70(2):145–175

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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. 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. Becchetti L, Leonardi S (2004) Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. J ACM 51:517–539

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Borodin A, Irani S, Raghavan P, Schieber B (1995) Competitive paging with locality of reference. J Comput Syst Sci 50(2):244–258

    Article  MathSciNet  MATH  Google Scholar 

  12. Borodin A, Linial N, Saks ME (1992) An optimal on-line algorithm for metrical task systems. J ACM 39(4):745–763

    Article  MathSciNet  MATH  Google Scholar 

  13. Chandra B (1992) Does randomization help in on-line bin packing? Inf Process Lett 43(1):15–19

    Article  MATH  Google Scholar 

  14. Coffman EG Jr, Gilbert EN (1985) On the expected relative performance of list scheduling. Oper Res 33(3):548–561

    Article  MathSciNet  MATH  Google Scholar 

  15. Coffman EG Jr, So K, Hofri M, Yao AC (1980) A stochastic model of bin-packing. Inf Control 44:105–115

    Article  MathSciNet  MATH  Google Scholar 

  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. 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

    Article  MathSciNet  MATH  Google Scholar 

  18. Correa J, Wagner M (2009) LP-based online scheduling: from single machine to parallel machines. Math Program 119(1):109–136

    Article  MathSciNet  MATH  Google Scholar 

  19. Csirik J, Johnson DS (2001) Bounded space on-line bin packing: best is better than first. Algorithmica 11:115–138

    Article  MathSciNet  Google Scholar 

  20. Fiat A, Karp RM, Luby M, McGeoch LA, Sleator DD, Young NE (1991) Competitive paging algorithms. J Algorithms 12:685–699

    Article  MATH  Google Scholar 

  21. Franaszek PA, Wagner TJ (1974) Some distribution-free aspects of paging algorithm performance. J ACM 21(1):31–39

    Article  MathSciNet  MATH  Google Scholar 

  22. Graham RL (1966) Bounds for certain multiprocessor anomalies. Bell Syst Tech J 45:1563–1581

    Google Scholar 

  23. Hiller B (2009) Online optimization: probabilistic analysis and algorithm engineering. PhD thesis, TU Berlin

  24. Hiller B, Vredeveld T (2008) On the optimality of least recently used. ZIB-Report 08-39, Zuse Institute Berlin

  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. 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. Johnson DS (1974) Fast algorithms for bin packing. J Comput Syst Sci 8(8):272–314

    Article  MATH  Google Scholar 

  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

    Article  MathSciNet  Google Scholar 

  29. Kalyanasundaram B, Pruhs K (2000) Speed is as powerful as clairvoyance. J ACM 47(4):617–643

    Article  MathSciNet  MATH  Google Scholar 

  30. Karlin AR, Manasse MS, Rudolph L, Sleator DD (1988) Competitive snoopy caching. Algorithmica 3:70–119

    Article  MathSciNet  Google Scholar 

  31. Karlin AR, Phillips SJ, Raghavan P (2000) Markov paging. SIAM J Comput 30(2):906–922

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Lee CC, Lee DT (1985) A simple online bin-packing algorithm. J ACM 32(3):562–572

    Article  MATH  Google Scholar 

  36. McGeoch LA, Sleator DD (1991) A strongly competitive randomized paging algorithm. Algorithmica 6:816–825

    Article  MathSciNet  MATH  Google Scholar 

  37. Möhring RH, Schulz AS, Uetz M (1999) Approximation in stochastic scheduling: the power of LP-based priority policies. J ACM 46:924–942

    Article  MathSciNet  MATH  Google Scholar 

  38. Motwani R, Phillips S, Torng E (1994) Non-clairvoyant scheduling. Theor Comput Sci 130:17–47

    Article  MathSciNet  MATH  Google Scholar 

  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

    Chapter  Google Scholar 

  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. Richey MB (1991) Improved bounds for harmonic-based bin packing algorithms. Discrete Appl Math 34(1–3):203–227

    Article  MathSciNet  MATH  Google Scholar 

  42. Scharbrodt M, Schickinger T, Steger A (2006) A new average case analysis for completion time scheduling. J. ACM 121–146

  43. Schrage L (1968) A proof of the optimality of the shortest remaining processing time discipline. Oper Res 16:687–690

    Article  MATH  Google Scholar 

  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. Shor PW (1986) The average-case analysis of some on-line algorithms for bin packing. Combinatorica 6(2):179–200

    Article  MathSciNet  MATH  Google Scholar 

  46. Sleator DD, Tarjan RE (1985) Amortized efficiency of list update and paging rules. Commun ACM 28(2):202–208

    Article  MathSciNet  Google Scholar 

  47. Souza A (2010) Adversarial models in paging—bridging the gap between theory and practice. Comput Sci Res Dev, this issue

  48. Souza A, Steger A (2006) The expected competitive ratio for weighted completion time scheduling. Theory Comput Syst 39:121–136

    Article  MathSciNet  MATH  Google Scholar 

  49. Spielman DA, Teng SH (2004) Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. J ACM 51:385–463

    Article  MathSciNet  MATH  Google Scholar 

  50. Torng E (1998) A unified analysis of paging and caching. Algorithmica 20(1):175–200

    Article  MathSciNet  MATH  Google Scholar 

  51. van Vliet A (1996) On the asymptotic worst case behavior of harmonic fit. J Algorithms 20(1):113–136

    Article  MathSciNet  MATH  Google Scholar 

  52. Vestjens APA (1997) On-line machine scheduling. PhD thesis, Eindhoven University of Technology, Netherlands

  53. Vredeveld T (2010) Stochastic online scheduling. Comput Sci Res Dev, this issue

  54. Yao AC (1980) New algorithms for bin packing. J ACM 27(2):207–227

    Article  MATH  Google Scholar 

  55. Young NE (1994) The k-server dual and loose competitiveness for paging. Algorithmica 11(6):525–541

    Article  MathSciNet  Google Scholar 

  56. Young NE (2000) On-line paging against adversarially biased random inputs. J Algorithms 37(1):218–235

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Correspondence to Benjamin Hiller.

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Work of B. Hiller partially supported by the DFG research group “Algorithms, Structure, Randomness” (Grant number GR 883/10-3, GR 883/10-4) and the DFG research center Matheon Berlin.

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Hiller, B., Vredeveld, T. Probabilistic alternatives for competitive analysis. Comput Sci Res Dev 27, 189–196 (2012). https://doi.org/10.1007/s00450-011-0149-1

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