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Online Bounded Analysis

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Computer Science – Theory and Applications (CSR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9691))

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Abstract

Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance measures, in particular targeted at what seems to be the core problem with competitive analysis: the comparison of the performance of an online algorithm is made to a too powerful adversary. We consider a new approach to restricting the power of the adversary, by requiring that when judging a given online algorithm, the optimal offline algorithm must perform as well as the online algorithm, not just on the entire final request sequence, but also on any prefix of that sequence. This is limiting the adversary’s usual advantage of being able to exploit that it knows the sequence is continuing beyond the current request. Through a collection of online problems, including machine scheduling, bin packing, dual bin packing, and seat reservation, we investigate the significance of this particular offline advantage.

Supported in part by the Danish Council for Independent Research, Natural Sciences, and the Villum Foundation.

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References

  1. Albers, S.: On the influence of lookahead in competitive paging algorithms. Algorithmica 18, 283–305 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Albers, S., Favrholdt, L.M., Giel, O.: On paging with locality of reference. In: 34th Annual ACM Symposium on the Theory of Computing (STOC), pp. 258–267 (2002)

    Google Scholar 

  3. Angelopoulos, S., Dorrigiv, R., López-Ortiz, A.: On the separation and equivalence of paging strategies. In: 18th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 229–237 (2007)

    Google Scholar 

  4. Azar, Y., Boyar, J., Epstein, L., Favrholdt, L.M., Larsen, K.S., Nielsen, M.N.: Fair versus unrestricted bin packing. Algorithmica 34(2), 181–196 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Azar, Y., Epstein, L.: On-line machine covering. J. Sched. 1(2), 67–77 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Azar, Y., Regev, O.: On-line bin-stretching. Theoret. Comput. Sci. 268(1), 17–41 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bansal, N., Sviridenko, M.: The Santa Claus problem. In: 38th Annual ACM Symposium on the Theory of Computing (STOC), pp. 31–40 (2006)

    Google Scholar 

  8. Ben-David, S., Borodin, A.: A new measure for the study of on-line algorithms. Algorithmica 11(1), 73–91 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Boyar, J., Epstein, L., Favrholdt, L.M., Larsen, K.S., Levin, A.: Online bounded analysis. CoRR, abs/1602.06708 (2016)

    Google Scholar 

  11. Boyar, J., Favrholdt, L., Mikkelsen, J., Kudahl, C.: Advice complexity for a class of online problems. In: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS). Leibniz International Proceedings in Informatics, vol. 30, pp. 116–129 (2015)

    Google Scholar 

  12. Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line algorithms. ACM Trans. Algorithms 3(2), 24 (2007). article 22

    Article  MathSciNet  MATH  Google Scholar 

  13. Boyar, J., Favrholdt, L.M., Larsen, K.S., Nielsen, M.N.: Extending the accommodating function. Acta Informatica 40(1), 3–35 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Boyar, J., Larsen, K.: The seat reservation problem. Algorithmica 25, 403–417 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Boyar, J., Larsen, K.S., Nielsen, M.N.: The accommodating function–a generalization of the competitive ratio. SIAM J. Comput. 31(1), 233–258 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Breslauer, D.: On competitive on-line paging with lookahead. Theoret. Comput. Sci. 209(1–2), 365–375 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chan, S.-H., Lam, T.-W., Lee, L.-K., Liu, C.-M., Ting, H.-F.: Sleep management on multiple machines for energy and flow time. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 219–231. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Cho, Y., Sahni, S.: Bounds for list schedules on uniform processors. SIAM J. Comput. 9(1), 91–103 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  19. Csirik, J., Totik, V.: On-line algorithms for a dual version of bin packing. Discrete Appl. Math. 21, 163–167 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  20. Dorrigiv, R., López-Ortiz, A., Munro, J.I.: On the relative dominance of paging algorithms. Theoret. Comput. Sci. 410, 3694–3701 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ehmsen, M.R., Kohrt, J.S., Larsen, K.S.: List factoring and relative worst order analysis. Algorithmica 66(2), 287–309 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Epstein, L.: Tight bounds for bandwidth allocation on two links. Discrete Appl. Math. 148(2), 181–188 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Epstein, L., Favrholdt, L.M., Kohrt, J.S.: Separating online scheduling algorithms with the relative worst order ratio. J. Comb. Optim. 12(4), 363–386 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. Epstein, L., Noga, J., Seiden, S.S., Sgall, J., Woeginger, G.J.: Randomized online scheduling on two uniform machines. In: Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 317–326 (1999)

    Google Scholar 

  25. Giannakopoulos, Y., Koutsoupias, E.: Competitive analysis of maintaining frequent items of a stream. Theoret. Comput. Sci. 562, 23–32 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)

    Article  MATH  Google Scholar 

  27. Karlin, A.R., Manasse, M.S., Rudolph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3, 79–119 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  28. Karlin, A.R., Phillips, S.J., Raghavan, P.: Markov paging. SIAM J. Comput. 30(3), 906–922 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  29. Kenyon, C.: Best-fit bin-packing with random order. In: 7th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 359–364 (1996)

    Google Scholar 

  30. Koutsoupias, E., Papadimitriou, C.H.: Beyond competitive analysis. In: 35th Annual Symposium on Foundations of Computer Science (FOCS), pp. 394–400 (1994)

    Google Scholar 

  31. Koutsoupias, E., Papadimitriou, C.H.: Beyond competitive analysis. SIAM J. Comput. 30(1), 300–317 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  32. Miyazaki, S., Okamoto, K.: Improving the competitive ratios of the seat reservation problem. In: Calude, C.S., Sassone, V. (eds.) TCS 2010. IFIP AICT, vol. 323, pp. 328–339. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  33. Raghavan, P.: A statistical adversary for on-line algorithms. In: On-Line Algorithms. Series in Discrete Mathematics and Theoretical Computer Science, vol. 7, pp. 79–83. American Mathematical Society (1992)

    Google Scholar 

  34. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  35. Woeginger, G.J.: A polynomial-time approximation scheme for maximizing the minimum machine completion time. Oper. Res. Lett. 20(4), 149–154 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  36. Young, N.: Competitive paging and dual-guided algorithms for weighted caching and matching (thesis). Technical Report CS-TR-348-91, Computer Science Department, Princeton University (1991)

    Google Scholar 

  37. Young, N.E.: The \(k\)-server dual and loose competitiveness for paging. Algorithmica 11, 525–541 (1994)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Joan Boyar, Lene M. Favrholdt & Kim S. Larsen

  2. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

  3. Faculty of IE&M, The Technion, Haifa, Israel

    Asaf Levin

Authors
  1. Joan Boyar
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  2. Leah Epstein
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  3. Lene M. Favrholdt
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  4. Kim S. Larsen
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  5. Asaf Levin
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Corresponding author

Correspondence to Kim S. Larsen .

Editor information

Editors and Affiliations

  1. Russian Academy of Sciences, St. Petersburg, Russia

    Alexander S. Kulikov

  2. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Boyar, J., Epstein, L., Favrholdt, L.M., Larsen, K.S., Levin, A. (2016). Online Bounded Analysis. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_10

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  • DOI: https://doi.org/10.1007/978-3-319-34171-2_10

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