Search theory

The terms search and search theory often include a wide variety of topics such as search through data bases, search for the maximum of a function, and search for a job. For this article, we limit our discussion to topics that are based on the classical search problem where there is one target that a “searcher” wishes to detect in an efficient manner. The searcher's knowledge about the target's location is represented by a probability distribution. There is a detection sensor whose performance is characterized by a function that relates search effort placed in a region to the probability of detecting the target given it is in that region. The searcher has a limited amount of effort and wishes to allocate this effort to maximize the probability of detecting the target.

In mathematical terms, the problem is formulated as follows: let

X =:

the search space (typically n-dimensional Euclidean space);

p(x) =:

the prior probability (density) of the target being located at x for x ∈ X;

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