Optimal unbounded search strategies

  • J. C. Raoult
  • J. Vuillemin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


We present here strategies for searching the (unique) zero of a real function, or its n-th derivative; we assume no a priori bound on the value x of this zero. The proposed strategy performs logry + llogry+ ... +1 + log*ry evaluations of f to determine x = ɛy with error less than ɛ (here r depends only on n). An argument of slowly converning integrals shows that these strategies are essentially optimal.


Binary Search External Node Prefix Code Unbounded Case Unimodular Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. J.L. BENTLEY & A.C. YAO [76]: An almost optimal algorithm for unbounded searching, IPL, vol. 3, no 3 (1976) pp. 82–87.Google Scholar
  2. N. BOURBAKI [76]: Théorie des fonctions de variables réelles, ch. V, app. no 8 (1976 3rd ed.), Hermann Paris.Google Scholar
  3. S. EILENBERG [74]: Automata, languages, and machines, Vol. A, Academic Press (1974).Google Scholar
  4. P. ELIAS [75]: Universal codework sets and representation of the integers, IEEE Trans. on Information theory, IT-21 (1975) pp. 194–203.Google Scholar
  5. S. EVEN & M. RODEH [78]: Economical encoding of commas between strings, CACM, Vol. 21, no 4 (1978) pp. 315–317.Google Scholar
  6. L. HYAFIL [77]: Optimal search for the zero of the n th derivative, IRIA/LABORIA, Rapport no 247 (1977).Google Scholar
  7. R.M. KARP & W.L. MIRANKER [72]: Parallel minimax search for a maximum, J. of Comb. Theory 4 (1972) pp. 19–35.Google Scholar
  8. H.P. KATSEFF [78]: Complexity dip in random infinite binary sequences, SIGACT Newsletters (Winter 1978) pp. 22–23.Google Scholar
  9. J. KIEFER [53]: Sequential minimax search for a maximum, Proc. Ameri. Soc. 4 (1953) pp. 502–506.Google Scholar
  10. D.E. KNUTH [75]: The art of computer programming, Vol. 3, Sorting and searching, Addison-Wesley (1975).Google Scholar
  11. D.E. KNUTH [79]: Supernatural numbers. (Dedicated to Martin Gardner).Google Scholar
  12. A. KOLMOGOROV [68]: Three approaches for defining the concept of information quantity, Selected Translations in Math. Stat. and Prob., AMS Publication (1968).Google Scholar
  13. H.T. KUNG [76]: Synchronized and asynchronous parallel algorithms for multi-processors, in Proc. of a Symp. on Algorithms and Complexity (1976). Edited by J.F. Traub, Academic Press, 1976, pp. 153–200.Google Scholar
  14. J. LINN [73]: General methods for parallel searching, Tech. Rep. no 61, Digital Systems Lab., Stanford University (1973).Google Scholar
  15. P. MARTIN-LÖF [71]: Complexity oscillations in infinite binary sequences, Z. Wahrsheinlichkeitstheorie Verw. Geb. 19 (1971) pp. 225–230.Google Scholar
  16. J.C. RAOULT, J. VUILLEMIN [79]: Optimal unbounded search strategies, Rapport LRI, no 33 (1979).Google Scholar
  17. R.L. RIVEST, A.R. MEYER, D.J. KLEITMAN, J. SPENCER, K. WINKLMAN [78]: Coping with errors in binary search procedures, Proc. of the 10th annual ACM Symposium on Theory of Computing, San Diego (1978) pp. 227–232.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • J. C. Raoult
    • 1
  • J. Vuillemin
    • 1
  1. 1.Laboratoire de Recherche en InformatiqueUniversité de Paris-SudORSAYFrance

Personalised recommendations