Advice Complexity of the Online Search Problem

  • Jhoirene Clemente
  • Juraj Hromkovič
  • Dennis Komm
  • Christian Kudahl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9843)

Abstract

The online search problem is a fundamental problem in finance. The numerous direct applications include searching for optimal prices for commodity trading and trading foreign currencies. In this paper, we analyze the advice complexity of this problem. In particular, we are interested in identifying the minimum amount of information needed in order to achieve a certain competitive ratio. We design an algorithm that reads b bits of advice and achieves a competitive ratio of \((M/m)^{1/(2^b+1)}\) where M and m are the maximum and minimum price in the input. We also give a matching lower bound. Furthermore, we compare the power of advice and randomization for this problem.

References

  1. 1.
    Barhum, K., Böckenhauer, H.-J., Forišek, M., Gebauer, H., Hromkovič, J., Krug, S., Smula, J., Steffen, B.: On the power of advice and randomization for the disjoint path allocation problem. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds.) SOFSEM 2014. LNCS, vol. 8327, pp. 89–101. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  2. 2.
    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.Theor. Comput. Sci. 554, 95–108 (2014). Elsevier Science PublishersGoogle Scholar
  3. 3.
    Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R.: On the advice complexity of the k-server problem. In: Du, D.-Z., Zhang, G. (eds.) ICALP 2011. LNCS, vol. 6755, pp. 207–218. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: On the advice complexity of the online problem. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 331–340. Springer, Heidelberg (2013)Google Scholar
  5. 5.
    Böckenhauer, H.-J., Komm, D., Královič, R., Rossmanith, P.: The online knapsack problem: advice and randomization. Theor. Comput. Sci. 527, 61–72 (2014)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, New York (1998)MATHGoogle Scholar
  7. 7.
    Boyar, J., Larsen, K.S., Maiti, A.: A comparison of performance measures via online search. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds.) FAW-AAIM 2012. LNCS, vol. 7285, pp. 303–314. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Boyar, J., Favrholdt, L.M., Kudahl, C., Mikkelsen, J.W.: Advice complexity for a class of online problems. In: Proceedings of the 32nd Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics, vol. 30, pp. 116–129. Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)Google Scholar
  9. 9.
    Dobrev, S., Královič, R., Pardubská, D.: How much information about the future is needed? In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 247–258. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    El-Yaniv, R., Fiat, A., Karp, R., Turpin, G.: Optimal search and one-way trading online algorithms. Algorithmica 30, 101–139 (2001)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Emek, Y., Fraigniaud, P., Korman, A., Rosén, A.: Online computation with advice. Theor. Comput. Sci. 412(24), 2642–2656 (2011)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Gupta, S., Kamali, S., López-Ortiz, A.: On advice complexity of the k-server problem under sparse metrics. In: Moscibroda, T., Rescigno, A.A. (eds.) SIROCCO 2013. LNCS, vol. 8179, pp. 55–67. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Komm, D., Královič, R.: Advice complexity and barely random algorithms. Theor. Inform. Appl. (RAIRO) 45(2), 249–267 (2011)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Lorenz, J., Panagiotou, K., Steger, A.: Optimal algorithms for \(k\)-search with application in option pricing. Algorithmica 55(2), 311–328 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Mikkelsen, J.: Randomization can be as helpful as a glimpse of the future in online computation. CoRR, abs/1511.05886 (2015)Google Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Xu, Y., Zhang, W., Zheng, F.: Optimal algorithms for the online time series search problem. Theoret. Comput. Sci. 412(3), 192–197 (2011)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jhoirene Clemente
    • 1
  • Juraj Hromkovič
    • 2
  • Dennis Komm
    • 2
  • Christian Kudahl
    • 3
  1. 1.Department of Computer ScienceUniversity of the Philippines DilimanQuezon CityPhilippines
  2. 2.Department of Computer ScienceETH ZürichZürichSwitzerland
  3. 3.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark

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