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linear search

Linear search problems deals with locating an object hidden on a half line (“long road”) by an absent-minded robot which gather everything it sees (see, e.g. here for more details). A program for the robot is a sequence \(0<x_1<x_2<\ldots\) of excursions it takes until the object is found.

In the situation when the object is hidden at a random location with a known distribution function \(F\), the problem of finding an optimal trajectory can be translated into understanding the dynamics of certain area preserving mappings.…

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