Matching Algorithms

Detailed Description

This group contains the algorithms for calculating matchings in 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 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.

Classes
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...
class	MaxWeightedMatching< GR, WM >::BlossomIt
	Iterator for obtaining the nodes of a blossom. More...
class	MaxWeightedPerfectMatching< GR, WM >::BlossomIt
	Iterator for obtaining the nodes of a blossom. More...

Files
file	matching.h
	Maximum matching algorithms in general graphs.