In combinatorics, a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study planar graphs and was later used by Edmonds to characterize a class of optimization problems that can be solved by greedy algorithms. Around 1980, Korte and Lovász introduced the greedoid to further generalize this characterization of greedy algorithms; hence the name greedoid. Besides mathematical optimization, greedoids have also been connected to graph theory, language theory, order theory, and other areas of mathematics.
In combinatorics, a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study...
a maximal linearly independent subset Rank of a free module Rank of a greedoid, the maximal size of a feasible set Rank of a group, the smallest cardinality...
basis theorem Generating set of a group Base (topology) Change of basis Greedoid Normal basis Polynomial basis Radial basis function Standard basis Transcendence...
455). Björner, Anders; Ziegler, Günter M. (1992), "8. Introduction to greedoids" (PDF), in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics...
concerning the study of finite or countable discrete structures. Matroid Greedoid Ramsey theory Van der Waerden's theorem Hales–Jewett theorem Umbral calculus...
factorization of a function.Pages displaying wikidata descriptions as a fallback Greedoid – Set system used in greedy optimization Incidence structure – Abstract...
and their vertices (sets of size 1). In the context of matroids and greedoids, abstract simplicial complexes are also called independence systems. An...
orderings or sets Coxeter matroid – Group-theoretic generalization of matroids Greedoid – Set system used in greedy optimization Oriented matroid – Abstraction...
inclusion relation). Other examples of set families are independence systems, greedoids, antimatroids, and bornological spaces. Algebra of sets – Identities and...
Bron–Kerbosch algorithm Listing all elements of structures such as matroids and greedoids Several problems on graphs, e.g., enumerating independent sets, paths...
Serganova, V. V. (1987), "On the general definition of a matroid and a greedoid", Doklady Akademii Nauk SSSR (in Russian), 292 (1): 15–20, ISSN 0002-3264...
MR 1171114. Björner, Anders; Ziegler, Günter M. (1992), "Introduction to Greedoids", in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics...
which their name derives. Antimatroids can be viewed as a special case of greedoids and of semimodular lattices, and as a generalization of partial orders...
solutions; see greedoid and matroid embedding for more information. Korte and Lovász would generalize these ideas to objects called greedoids, which allow...
combinatorial algorithms, particularly the greedy algorithm. More generally, a greedoid is useful for studying the finite termination of algorithms. R. Tyrrell...
Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász, and Rainer Schrader, 1991, vol. 4) Mathematics...
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