# Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

# Search theory

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_929

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 xX;

f(x) =

the...

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