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Israel Journal of Mathematics

, Volume 53, Issue 3, pp 365–372 | Cite as

The linear search problem rides again

  • Anatole Beck
  • Micah Beck
Article

Abstract

The Linear Search Problem concerns a search for a point in the real line by continuous motion starting at 0. The optimal turning points for such a search under the hypothesis that the location of the target is distributed normally about 0 have been approximated by mechanical calculation, but no proof has been given that there is only a single minimizing strategy or that the numbers calculated do indeed approximate that strategy. Plausible arguments have been made before, both by these authors and others. In this paper, the plausible arguments are supplanted by mathematical proofs.

Keywords

Senior Author Mathematical Proof Digital Equipment Corporation Plausible Argument Normal Density 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.

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References

  1. 1.
    Anatole Beck,On the linear search problem, Isr. J. Math.2 (1964), 221–228.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Anatole Beck,More on the linear search problem, Isr. J. Math.3 (1965), 61–70.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Anatole Beck and D. J. Newman,Yet more on the linear search problem, Isr. J. Math.8 (1970), 419–429.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Anatole Beck and Peter Warren,The return of the linear search problem, Isr. J. Math.14 (1973), 503–512.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Anatole Beck and Micah Beck,Son of the linear search problem, Isr. J. Math.48 (1984), 109–122.MATHMathSciNetGoogle Scholar
  6. 6.
    Peter J. Rousseeuw,Optimal search paths for random variables, J. Comput. Appl. Math.9 (1983), 279–286.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1986

Authors and Affiliations

  • Anatole Beck
    • 1
    • 2
    • 3
  • Micah Beck
    • 1
    • 2
    • 3
  1. 1.University of WisconsinMadisonUSA
  2. 2.London School of Economics and Political ScienceUniversity of LondonUK
  3. 3.Cornell UniversityIthacaUSA

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