Skip to main content
SpringerLink
Log in

On the List Update Problem with Advice

  • Conference paper
Language and Automata Theory and Applications (LATA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8370))

Abstract

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than 15/14. On the other hand, we show that surprisingly two bits of advice is sufficient to break the lower bound of 2 on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of \(1.\bar{6}\). In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albers, S.: Improved randomized on-line algorithms for the list update problem. SIAM J. Comput. 27(3), 682–693 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Albers, S., von Stengel, B., Werchner, R.: A combined BIT and TIMESTAMP algorithm for the list update problem. Inf. Proc. Lett. 56, 135–139 (1995)

    Article  MATH  Google Scholar 

  3. Ambühl, C.: Offline list update is NP-hard. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 42–51. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  4. Bentley, J.L., Sleator, D., Tarjan, R.E., Wei, V.K.: A locally adaptive data compression scheme. Commun. ACM 29, 320–330 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  5. Böckenhauer, H.-J., Hromkovič, J., Komm, D., Krug, S., Smula, J., Sprock, A.: The string guessing problem as a method to prove lower bounds on the advice complexity. In: Du, D.-Z., Zhang, G. (eds.) COCOON 2013. LNCS, vol. 7936, pp. 493–505. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R.: On the advice complexity of the k-server problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 207–218. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Böckenhauer, H., 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)

    Chapter  Google Scholar 

  8. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)

    Google Scholar 

  9. Boyar, J., Kamali, S., Larsen, K.S., López-Ortiz, A.: Online bin packing with advice. CoRR abs/1212.4016 (2012)

    Google Scholar 

  10. Dobrev, S., Královič, R., Pardubská, D.: Measuring the problem relevant information in input. RAIRO Inform. Theor. Appl. 43(3), 585–613 (2009)

    Article  MATH  Google Scholar 

  11. Emek, Y., Fraigniaud, P., Korman, A., Rosén, A.: Online computation with advice. Theoret. Comput. Sci. 412(24), 2642–2656 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hromkovič, J., Královič, R., Královič, R.: Information complexity of online problems. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 24–36. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Irani, S.: Two results on the list update problem. Inf. Proc. Lett. 38, 301–306 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kamali, S., López-Ortiz, A.: A survey of algorithms and models for list update. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds.) Ianfest-66. LNCS, vol. 8066, pp. 251–266. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Komm, D., Královič, R.: Advice complexity and barely random algorithms. RAIRO Inform. Theor. Appl. 45(2), 249–267 (2011)

    Article  MATH  Google Scholar 

  16. Reingold, N., Westbrook, J.: Optimum off-line algorithms for the list update problem. Tech. Rep. YALEU/DCS/TR-805, Yale University (1990)

    Google Scholar 

  17. Reingold, N., Westbrook, J.: Off-line algorithms for the list update problem. Inf. Proc. Lett. 60(2), 75–80 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Reingold, N., Westbrook, J., Sleator, D.D.: Randomized competitive algorithms for the list update problem. Algorithmica 11, 15–32 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Renault, M.P., Rosén, A.: On online algorithms with advice for the k-server problem. In: Solis-Oba, R., Persiano, G. (eds.) WAOA 2011. LNCS, vol. 7164, pp. 198–210. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    Joan Boyar & Kim S. Larsen

  2. School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Shahin Kamali & Alejandro López-Ortiz

Authors
  1. Joan Boyar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shahin Kamali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kim S. Larsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alejandro López-Ortiz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. School of Computer Science, Department of Software Engineering and Artificial Intelligence, Complutense University of Madrid, Professor José Garcia Santesmases, 9, 28040, Madrid, Spain

    José-Luis Sierra-Rodríguez

  3. Fakultät für Informatik, Institut für Wissens- und Sprachverarbeitung, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Bianca Truthe

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Boyar, J., Kamali, S., Larsen, K.S., López-Ortiz, A. (2014). On the List Update Problem with Advice. In: Dediu, AH., Martín-Vide, C., Sierra-Rodríguez, JL., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2014. Lecture Notes in Computer Science, vol 8370. Springer, Cham. https://doi.org/10.1007/978-3-319-04921-2_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-04921-2_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04920-5

  • Online ISBN: 978-3-319-04921-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation