Matroid embedding
0In combinatorics, a matroid embedding is a set system (F, E), where F is a collection of feasible sets, that satisfies the following properties:
(Accessibility Property) Every non-empty feasible set X contains an element x such that X\{x} is feasible;
(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;
(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 or no e in ext(X);
The collection of all subsets of feasible sets forms a matroid.Matroid embedding was introduced by Helman, Moret & Shapiro (1993) to characterize problems that can be optimized by a greedy algorithm.
Source: https://en.wikipedia.org/wiki/Matroid_embedding
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