Matroid embedding

In combinatorics, a matroid embedding is a set system (F, E), where F is a collection of feasible sets, that satisfies the following properties.
 * 1) Accessibility property: Every non-empty feasible set X contains an element x such that X \ {x} is feasible.
 * 2) Extensibility property: For every feasible subset X of a basis (i.e., maximal feasible set) B, some element in B but not in X belongs to the extension ext(X) of X, where ext(X) is the set of all elements e not in X such that X ∪ {e} is feasible.
 * 3) Closure–congruence property: For every superset A of a feasible set X disjoint from ext(X), A ∪ {e} is contained in some feasible set for either all e or no e in ext(X).
 * 4) The collection of all subsets of feasible sets forms a matroid.

Matroid embedding was introduced by to characterize problems that can be optimized by a greedy algorithm.