Search problem

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages) This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Search problem" – news · newspapers · books · scholar · JSTOR (May 2025) (Learn how and when to remove this message) This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (May 2025) (Learn how and when to remove this message) (Learn how and when to remove this message)

In computational complexity theory and computability theory, a search problem is a computational problem of finding an admissible answer for a given input value, provided that such an answer exists. In fact, a search problem is specified by a binary relation R where xRy if and only if "y is an admissible answer given x".^{[note 1]} Search problems frequently occur in graph theory and combinatorial optimization, e.g. searching for matchings, optional cliques, and stable sets in a given undirected graph.

An algorithm is said to solve a search problem if, for every input value x, it returns an admissible answer y for x when such an answer exists; otherwise, it returns any appropriate output, e.g. "not found" for x with no such answer.
Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).