minimumsete
Minimumsete is a term used in mathematical and computational contexts to denote a subset of a given universe that satisfies a specified condition and is chosen according to a criterion of minimality. Because the phrase is not universally standardized, its exact meaning can vary by discipline and problem formulation. Two common variants appear in literature.
Inclusion-minimal minimumsete: A subset S of a universal set X satisfies a property P, and no proper
Cardinality-minimal (minimum-cardinality) minimumsete: A subset S satisfies P and has the smallest possible size among all
Examples help illustrate the distinction. If P(S) requires S to intersect each class in a partition of
Applications of the concept include combinatorial optimization, logic simplification, database query minimization, and network design, where
Relation to related notions: The term overlaps with minimal sets and minimum elements in order theory. It
See also: Minimal set, Set cover, Hitting set, Cardinality, Basis.
References: General discussions of minimal and minimum subsets in combinatorics and algorithmic problem definitions.