Skip to main content
SpringerLink
Log in

Star search—A different show

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

An extension of the line search problem is considered in which the number of directions in which the searcher can head from the origin is arbitrary, but finite. One problem under study is when the distribution of the particle to be found has a bounded support. Sufficient conditions are established under which an optimal policy exhausts a given direction before it proceeds to another one, and the optimal order of directions in which to search is found. Special cases and some extensions are considered. A second problem has a game theoretic flavor, in particular a conjecture of Gal [13] is partially resolved.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Beck,On the linear search problem, Isr. J. Math.2 (1964), 221–228.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Beck,More on the linear search problem, Isr. J. Math.3 (1965), 61–70.

    Article  MathSciNet  Google Scholar 

  3. A. Beck and D. J. Newman,Yet more on the linear search problem, Isr. J. Math.8 (1970), 419–429.

    MATH  MathSciNet  Google Scholar 

  4. A. Beck and P. Warren,The return of the linear search problem, Isr. J. Math.14 (1973), 169–183.

    MATH  MathSciNet  Google Scholar 

  5. A. Beck and M. Beck,Son of the linear search problem, Isr. J. Math.48 (1984), 109–122.

    MATH  MathSciNet  Google Scholar 

  6. A. Beck and M. Beck,The linear search problem rides again, Isr. J. Math.53 (1986), 365–372.

    MATH  MathSciNet  Google Scholar 

  7. R. Bellman,Problem 63-9, An optimal search, SIAM Rev.5 (1963), 274.

    Article  Google Scholar 

  8. F. T. Bruss and J. B. Robertson,A survey of the linear search problem, Math. Sci.13 (1988), 75–89.

    MATH  MathSciNet  Google Scholar 

  9. R. W. Conway, W. L. Maxwell and L. W. Miller,Theory of Scheduling, Addison-Wesley, Reading Massachusetts, 1967.

    MATH  Google Scholar 

  10. W. Franck,An optimal search problem, SIAM Rev.7 (1965), 503–512.

    Article  MathSciNet  Google Scholar 

  11. B. Fristedt and D. Heath,Searching for a particle on the real line, Adv. Appl. Prob.6 (1974), 79–102.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Gal,Minimax solutions for linear search problems, SIAM J. Appl. Math27 (1974), 17–30.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Gal,Search Games, Academic Press, New York, 1980.

    MATH  Google Scholar 

  14. F. P. Kelly,A remark on search sequencing problems, Math. Opns. Res.7 (1982), 154–157.

    MATH  Google Scholar 

  15. G. Rau,Minimizing a function of permutations of n integers, Opns. Res.19 (1971), 237–240.

    Article  MATH  Google Scholar 

  16. P. J. Rousseeuw,Optimal search paths for random variables, J. Comput. Appl. Math.9 (1983), 279–286.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Author notes

  1. Offer Kella

    Present address: Department of Statistics, The Hebrew University of Jerusalem, Mt. Scopus, 91905, Jerusalem, Israel

Authors and Affiliations

    Authors
    1. Offer Kella
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Kella, O. Star search—A different show. Israel J. Math. 81, 145–159 (1993). https://doi.org/10.1007/BF02761302

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF02761302

    Keywords

    Search

    Navigation