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Minimum Cut Algorithms
Algorithms

## Detailed Description

This group contains the algorithms for finding minimum cut in graphs.

The minimum cut problem is to find a non-empty and non-complete subset of the nodes with minimum overall capacity on outgoing arcs. Formally, there is a digraph, a capacity function. The minimum cut is the solution of the next optimization problem:

LEMON contains several algorithms related to minimum cut problems:

- Hao-Orlin algorithm for calculating minimum cut in directed graphs.
- Nagamochi-Ibaraki algorithm for calculating minimum cut in undirected graphs.
- Gomory-Hu tree computation for calculating all-pairs minimum cut in undirected graphs.

If you want to find minimum cut just between two distinict nodes, see the maximum flow problem.

## Classes

class | GomoryHu< GR, CAP >
| Gomory-Hu cut tree algorithm. More...
class | HaoOrlin< GR, CAP, TOL >
| Hao-Orlin algorithm for finding a minimum cut in a digraph. More...
class | NagamochiIbaraki< GR, CM, TR >
| Calculates the minimum cut in an undirected graph. More...

## Files

file | gomory_hu.h
| Gomory-Hu cut tree in graphs.
file | hao_orlin.h
| Implementation of the Hao-Orlin algorithm.
file | nagamochi_ibaraki.h
| Implementation of the Nagamochi-Ibaraki algorithm.