Computing with Priced Information: When the Value Makes the Price

  • Ferdinando Cicalese
  • Martin Milanič
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

Abstract

We study the function evaluation problem in the priced information framework introduced in [Charikar et al. 2002]. We characterize the best possible extremal competitive ratio for the class of game tree functions. Moreover, we extend the above result to the case when the cost of reading a variable depends on the value of the variable. In this new value dependent cost variant of the problem, we also exactly evaluate the extremal competitive ratio for the whole class of monotone Boolean functions.

Keywords

Feasible Solution Boolean Function Polynomial Time Algorithm Competitive Ratio Price Information 
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.
    Boros, E., Ünlüyurt, T.: Diagnosing double regular systems. Annals of Mathematics and Artificial Intelligence 26(1-4), 171–191 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Charikar, M., Fagin, R., Guruswami, V., Kleinberg, J.M., Raghavan, P., Sahai, A.: Query strategies for priced information. Journal of Comp. and Syst. Sci. 64, 785–819 (2002)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Cicalese, F., Laber, E.S.: A new strategy for querying priced information. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing, pp. 674–683 (2005)Google Scholar
  4. 4.
    Cicalese, F., Laber, E.S.: An optimal algorithm for querying priced information: Monotone Boolean functions and game trees. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 664–676. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Cicalese, F., Laber, E.S.: On the competitive ratio of evaluating priced functions. In: Proc. of SODA 2006, pp. 944–953 (2006)Google Scholar
  6. 6.
    Cicalese, F., Laber, E.S.: Function evaluation via linear programming in the priced information model. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 173–185. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Cicalese, F., Milanič, M.: Computing with priced information: game trees and the value dependent cost model. Technical Report 2008-03, Technical Faculty, Bielefeld University (2008); Also available from the authors’ web sitesGoogle Scholar
  8. 8.
    Diderich, C.G.: A bibliography on minimax trees. SIGACT News 24(4), 82–89 (1993)CrossRefMATHGoogle Scholar
  9. 9.
    Duffuaa, S.O., Raouf, A.: An optimal sequence in multicharacteristics inspection. J. Optim. Theory Appl. 67(1), 79–86 (1990)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Gillies, D.W.: Algorithms to schedule tasks with and/or precedence constraints. PhD thesis, Champaign, IL, USA (1993)Google Scholar
  11. 11.
    Greiner, R., Hayward, R., Jankowska, M., Molloy, M.: Finding optimal satisficing strategies for and-or trees. Artificial Intelligence 170(1), 19–58 (2006)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Heiman, R., Wigderson, A.: Randomized vs. deterministic decision tree complexity for read-once boolean functions. Computational Complexity 1, 311–329 (1991)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Hellerstein, J.M.: Optimization techniques for queries with expensive methods. ACM Transactions on Database Systems 23(2), 113–157 (1998)CrossRefGoogle Scholar
  14. 14.
    Cox, J.L.A., Qiu, Y., Kuehner, W.: Heuristic least-cost computation of discrete classification functions with uncertain argument values. Ann. Oper. Res. 21(1-4), 1–30 (1989)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Qiu, Y., Cox Jr., L.A., Davis, L.: Guess-and-verify heuristics for reducing uncertainties in expert classification systems. In: Dubois, D., Wellman, M.P. (eds.) UAI, pp. 252–258. Morgan Kaufmann, San Francisco (1992)Google Scholar
  16. 16.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach. Prentice Hall, Englewood Cliffs (1995)MATHGoogle Scholar
  17. 17.
    Saks, M., Wigderson, A.: Probabilistic Boolean decision trees and the complexity of evaluating game trees. In: Proc. of FOCS 1986, pp. 29–38 (1986)Google Scholar
  18. 18.
    Shenoy, P.P.: Game trees for decision analysis. Theory and Decision 44, 149–171 (1998)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Snir, M.: Lower bounds on probabilistic linear decision trees. TCS 38(1), 69–82 (1985)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Tarsi, M.: Optimal search on some game trees. Journal of the ACM 30(3), 389–396 (1983)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Turney, P.: Types of cost in inductive concept learning. In: Proceedings of Workshop Cost-Sensitive Learning at the 17th International Conference on Machine Learning (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ferdinando Cicalese
    • 1
  • Martin Milanič
    • 1
  1. 1.AG Genominformatik, Faculty of TechnologyBielefeld UniversityGermany

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