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POLYMATROID

Polymatroid

Multiset analogue of matroids

In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also a generalization

Polymatroid

Jack Edmonds

American/Canadian mathematician and computer scientist

describes finite graphs from the point of view of matchings. He introduced polymatroids, submodular flows with Richard Giles, and the terms clutter and blocker

Jack Edmonds

Jack_Edmonds

Matroid parity problem

Largest independent set of paired elements

generalization of graph matching and matroid intersection. It is also known as polymatroid matching, or the matchoid problem. Matroid parity can be solved in polynomial

Matroid parity problem

Matroid_parity_problem

Linear programming

Method to solve optimization problems

submodular flow polyhedra, and the intersection of two generalized polymatroids/g-polymatroids – e.g. see Schrijver 2003. Permissive licenses: Copyleft (reciprocal)

Linear programming

Linear_programming

Matroid

Abstraction of linear independence of vectors

optimization Oriented matroid – Abstraction of ordered linear algebra Polymatroid – Multiset analogue of matroids Pregeometry (model theory) – Formulation

Matroid

Submodular set function

Set-to-real map with diminishing returns

diversity, information and coverage. Supermodular function Matroid, Polymatroid Utility functions on indivisible goods H. Lin and J. Bilmes, A Class

Submodular set function

Submodular_set_function

Matroid polytope

Convex hull of indicator vectors of bases

{\displaystyle M} , the independence matroid polytope is equal to the polymatroid determined by ψ {\displaystyle \psi } . The flag matroid polytope is

Matroid polytope

Matroid_polytope

Greedoid

Set system used in greedy optimization

can be explained by taking the line search greedoid instead. Matroid Polymatroid Note that the accessibility property is strictly weaker than the hereditary

Greedoid

Nash equilibrium computation

Economical computational problem

and Peis present a pseudo-polytime algorithm that computes a PNE for polymatroid CGs[clarification needed] with player-specific delay functions and polynomially-bounded

Nash equilibrium computation

Nash_equilibrium_computation

Congestion game

Class of games in game theory

and Timmermans also study equilibrium uniqueness in atomic splittable polymatroid CGs. Marcotte presented four numeric algorithms for computing NE on congested

Congestion game

Congestion_game