Matroid embedding


In combinatorics, a matroid embedding is a set system, 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 \ is feasible.
  2. Extensibility property: For every feasible subset X of a basis ''B, some element in B'' but not in X belongs to the extension ext of X, where ext is the set of all elements e not in X such that X ∪ is feasible.
  3. Closure–congruence property: For every superset A of a feasible set X disjoint from ext, A ∪ is contained in some feasible set for either all e or no e in ext.
  4. The collection of all subsets of feasible sets forms a matroid.
Matroid embeddings were introduced by to characterize problems that can be optimized by a greedy algorithm.