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Advice Complexity and Barely Random Algorithms

  • Dennis Komm
  • Richard Královič
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6543)

Abstract

Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our special focus goes to barely random algorithms, i.e., randomized algorithms that use only a constant number of random bits, regardless of the input size. We adapt the results on advice complexity to obtain efficient barely random algorithms for both the job shop scheduling and the paging problem.

Furthermore, so far, it has not been investigated for job shop scheduling how good an online algorithm may perform when only using a very small (e.g., constant) number of advice bits. In this paper, we answer this question by giving both lower and upper bounds, and also improve the best known upper bound for optimal algorithms.

Keywords

Competitive Ratio Online Algorithm Random Algorithm Physical Memory Page Fault 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Achlioptas, D., Chrobak, M., Noga, J.: Competitive analysis of randomized paging algorithms. Theoretical Computer Science 234(1–2), 203–218 (2000)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: On the advice complexity of online problems. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 331–340. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: Online Algorithms with Advice. Technical Report 614. ETH Zurich, Department of Computer Science (2009)Google Scholar
  4. 4.
    Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press, New York (1998)MATHGoogle Scholar
  5. 5.
    Brucker, P.: An efficient algorithm for the job-shop problem with two jobs. Computing 40(4), 353–359 (1988)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Dobrev, S., Královič, R., Pardubská, D.: How much information about the future is needed? In: 34th Conf. on Current Trends in Theory and Practice of Computer Science (SOFSEM 2008), pp. 247–258 (2008)Google Scholar
  7. 7.
    Emek, Y., Fraigniaud, P., Korman, A., Rosén, A.: Online computation with advice. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 427–438. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Hromkovič, J., Mömke, T., Steinhöfel, K., Widmayer, P.: Job shop scheduling with unit length tasks: bounds and algorithms. Algorithmic Operations Research 2(1), 1–14 (2007)MathSciNetMATHGoogle Scholar
  9. 9.
    Hromkovič, J.: Design and Analysis of Randomized Algorithms: Introduction to Design Paradigms. Springer, New York (2006)MATHGoogle Scholar
  10. 10.
    Komm, D., Královič, R.: Advice Complexity and Barely Random Algorithms. Technical Report 684. ETH Zurich, Department of Computer Science (2010)Google Scholar
  11. 11.
    Mömke, T.: On the power of randomization for job shop scheduling with k-units length tasks. RAIRO Theoretical Informatics and Applications 43, 189–207 (2009)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Reingold, N., Westbrook, J., Sleator, D.: Randomized competitive algorithms for the list update problem. Algorithmica 11(1), 15–32 (1994)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dennis Komm
    • 1
  • Richard Královič
    • 1
  1. 1.Department of Computer ScienceETH ZurichSwitzerland

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