# Polymatroid

## Related Groups

- submodular

## Type

- definition
- relation

## Statement

Polymatroid la object polyhedral gan voi rank function submodular, tong quat hoa viewpoint matroid theo cach phu hop voi optimization. Day la mot ngon ngu structural quan trong de noi submodularity voi polyhedra va linear optimization.

## Intuition

Neu matroid cho ta mot abstraction ve independence, thi polymatroid cho ta mot abstraction "mem" hon cho rank-based structure. Nhieu ket qua ve greedy, rank, va polyhedral optimization tro nen de nhin hon khi dua ve ngon ngu polymatroid.

## Equivalent Views

- polyhedral viewpoint
- rank-function viewpoint

## Standard Examples

- rank polytope / polymatroid giai thich boi Edmonds
- cac rank-based constructions tu matroid theory

## Related Results

- paper Edmonds la diem goc trung tam
- rat nhieu ket qua sau nay trong submodular optimization an structure polymatroid o hau truong

## Where It Is Used

- `1970-edmonds-submodular-functions-matroids-polyhedra`
- survey ve foundations / minimization