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Minimum Cut 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 $X$ subset of the nodes with minimum overall capacity on outgoing arcs. Formally, there is a $G=(V,A)$ digraph, a $cap: A\rightarrow\mathbf{R}^+_0$ capacity function. The minimum cut is the $X$ solution of the next optimization problem:

\[ \min_{X \subset V, X\not\in \{\emptyset, V\}} \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \]

LEMON contains several algorithms related to minimum cut problems:

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


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...


file  gomory_hu.h

Gomory-Hu cut tree in graphs.

file  hao_orlin.h

Implementation of the Hao-Orlin algorithm.

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