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Matching Algorithms
Algorithms

## Detailed Description

This group contains the algorithms for calculating matchings in graphs and bipartite graphs. The general matching problem is finding a subset of the edges for which each node has at most one incident edge.

There are several different algorithms for calculate matchings in graphs. The matching problems in bipartite graphs are generally easier than in general graphs. The goal of the matching optimization can be finding maximum cardinality, maximum weight or minimum cost matching. The search can be constrained to find perfect or maximum cardinality matching.

The matching algorithms implemented in LEMON:

- MaxMatching Edmond's blossom shrinking algorithm for calculating maximum cardinality matching in general graphs.
- MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating maximum weighted matching in general graphs.
- MaxWeightedPerfectMatching Edmond's blossom shrinking algorithm for calculating maximum weighted perfect matching in general graphs.
- MaxFractionalMatching Push-relabel algorithm for calculating maximum cardinality fractional matching in general graphs.
- MaxWeightedFractionalMatching Augmenting path algorithm for calculating maximum weighted fractional matching in general graphs.
- MaxWeightedPerfectFractionalMatching Augmenting path algorithm for calculating maximum weighted perfect fractional matching in general graphs.

## Classes

class | MaxFractionalMatching< GR, TR >
| Max cardinality fractional matching. More...
class | MaxWeightedFractionalMatching< GR, WM >
| Weighted fractional matching in general graphs. More...
class | MaxWeightedPerfectFractionalMatching< GR, WM >
| Weighted fractional perfect matching in general graphs. More...
class | MaxMatching< GR >
| Maximum cardinality matching in general graphs. More...
class | MaxWeightedMatching< GR, WM >
| Weighted matching in general graphs. More...
class | MaxWeightedPerfectMatching< GR, WM >
| Weighted perfect matching in general graphs. More...

## Files

file | fractional_matching.h
file | matching.h