Optimal Whereabouts Search

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Abstract
An optimal whereabouts search maximizes the probability of correctly stating, at the end of a search costing no more than some budget C, which box contains the object. This can be accomplished either by finding the object in the search or by guessing, at the end of an unsuccessful search, which box contains the object. Generalizing work of Tognetti, this paper shows that an optimal whereabouts search never searches the box to be guessed, and gives an algorithm for finding an optimal whereabouts-search strategy. Finally, whereabouts search is compared to a similar problem proposed by Bellman.

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