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Searching for a particle on the real line

Published online by Cambridge University Press:  01 July 2016

Bert Fristedt  and
David Heath
Bert Fristedt
Affiliation:
University of Minnesota, Minneapolis
David Heath
Affiliation:
University of Minnesota, Minneapolis
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Abstract

In this paper we consider two optimization problems and two game problems. In each problem, a particle is hidden on the real line (sometimes randomly, and sometimes by an antagonistic hider), and a seeker, starting at the origin, wishes to find the particle with minimal expected cost. We consider a fairly wide class of cost functions depending upon the position of the particle and the time used to discover it. For the games we obtain the values and (∊-) optimal strategies. For the optimization problems we obtain qualitative features of (∊-) optimal searches.

Keywords

LINEAR SEARCH PROBLEMOPTIMAL SEARCHSEEKERHIDERSEARCH GAMEHIDING GAMEOPTIMAL HIDING
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 79 - 102
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Beck, A. (1964) On the linear search problem. Israeli. Math. 2, 221–228.CrossRefGoogle Scholar
[2] Beck, A. (1965) More on the linear search problem. Israel J. Math. 3, 61–70.Google Scholar
[3] Beck, A. and Newman, D. J. (1970) Yet more on the linear search problem. Israel J. Math. 8, 419–429.Google Scholar
[4] Beck, A. and Warren, P. (1973) The return of the linear search problem. Israel J. Math. 14, 169–183.CrossRefGoogle Scholar
[5] Franck, W. (1965) On an optimal search problem. SIAM Rev. 7, 503–512.Google Scholar
[6] Gal, S. (1973) Minimax solutions for linear search problems. Preprint from the Department of Statistics, Tel-Aviv University.Google Scholar