The generalized linear search problem. Existence of optimal search paths. (English) Zbl 0642.90061

The linear search problem deals with searching for a hidden target x on the real line the position of which is given by the value of a random variable X. A searcher looks for x from a starting point, with an upper bound on his speed and using a continuous path. The author generalizes previous work by A. Beck [Isr. J. Math. 2, 221-228 (1964; Zbl 0168.395)] in the sense that an arbitrary point on the real line (and not only the origin) can be used as the starting point. The conditions on the distribution of X under which the expected cost can be minimized (i.e. the optimal search paths exist) are given. Some possible applications of the linear search problem are mentioned.
Reviewer: T.Cipra


90B40 Search theory


Zbl 0168.395
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