A General Framework for Searching on a Line

Consider the following classical search problem: a target is located on the line at distance D from the origin. Starting at the origin, a searcher must find the target with minimum competitive cost. The classical competitive cost studied in the literature is the ratio between the distance travelled by the searcher and D. Note that when no lower bound on D is given, no competitive search strategy exists for this problem. Therefore, all competitive search strategies require some form of lower bound on D.

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