MaxMatching< GR > Class Template Reference

Detailed Description

template<typename GR>
class lemon::MaxMatching< GR >

This class implements Edmonds' alternating forest matching algorithm for finding a maximum cardinality matching in a general undirected graph. It can be started from an arbitrary initial matching (the default is the empty one).

The dual solution of the problem is a map of the nodes to Status, having values EVEN (or D), ODD (or A) and MATCHED (or C) defining the Gallai-Edmonds decomposition of the graph. The nodes in EVEN/D induce a subgraph with factor-critical components, the nodes in ODD/A form the canonical barrier, and the nodes in MATCHED/C induce a graph having a perfect matching. The number of the factor-critical components minus the number of barrier nodes is a lower bound on the unmatched nodes, and the matching is optimal if and only if this bound is tight. This decomposition can be obtained using status() or statusMap() after running the algorithm.

Template Parameters

GR	The undirected graph type the algorithm runs on.

#include <lemon/matching.h>

Public Types
enum	Status { EVEN = 1 , MATCHED = 0 , ODD = -1 , UNMATCHED = -2 }
	Status constants for Gallai-Edmonds decomposition. More...
typedef GR	Graph
	The graph type of the algorithm.
typedef Graph::template NodeMap< typename Graph::Arc >	MatchingMap
	The type of the matching map.
typedef Graph::template NodeMap< Status >	StatusMap
	The type of the status map.

Public Member Functions
	MaxMatching (const Graph &graph)
Execution Control
The simplest way to execute the algorithm is to use the run() member function. If you need better control on the execution, you have to call one of the functions init(), greedyInit() or matchingInit() first, then you can start the algorithm with startSparse() or startDense().
void	init ()
	Set the initial matching to the empty matching.
void	greedyInit ()
	Find an initial matching in a greedy way.
template<typename MatchingMap >
bool	matchingInit (const MatchingMap &matching)
	Initialize the matching from a map.
void	startSparse ()
	Start Edmonds' algorithm.
void	startDense ()
	Start Edmonds' algorithm with a heuristic improvement for dense graphs.
void	run ()
	Run Edmonds' algorithm.
Primal Solution
Functions to get the primal solution, i.e. the maximum matching.
int	matchingSize () const
	Return the size (cardinality) of the matching.
bool	matching (const Edge &edge) const
	Return true if the given edge is in the matching.
Arc	matching (const Node &n) const
	Return the matching arc (or edge) incident to the given node.
const MatchingMap &	matchingMap () const
	Return a const reference to the matching map.
Node	mate (const Node &n) const
	Return the mate of the given node.
Dual Solution
Functions to get the dual solution, i.e. the Gallai-Edmonds decomposition.
Status	status (const Node &n) const
	Return the status of the given node in the Edmonds-Gallai decomposition.
const StatusMap &	statusMap () const
	Return a const reference to the status map, which stores the Edmonds-Gallai decomposition.
bool	barrier (const Node &n) const
	Return true if the given node is in the barrier.

Member Enumeration Documentation

enum Status

These constants are used for indicating the Gallai-Edmonds decomposition of a graph. The nodes with status EVEN (or D) induce a subgraph with factor-critical components, the nodes with status ODD (or A) form the canonical barrier, and the nodes with status MATCHED (or C) induce a subgraph having a perfect matching.

Enumerator:

EVEN	= 1. (D is an alias for EVEN.)
MATCHED	= 0. (C is an alias for MATCHED.)
ODD	= -1. (A is an alias for ODD.)
UNMATCHED	= -2.

Constructor & Destructor Documentation

MaxMatching ( const Graph &  graph )

inline

Constructor.

Member Function Documentation

void init ( )

inline

This function sets the initial matching to the empty matching.

void greedyInit ( )

inline

This function finds an initial matching in a greedy way.

bool matchingInit ( const MatchingMap &  matching )

inline

This function initializes the matching from a bool valued edge map. This map should have the property that there are no two incident edges with true value, i.e. it really contains a matching.

Returns

true if the map contains a matching.

void startSparse ( )

inline

This function runs the original Edmonds' algorithm.

Precondition

init(), greedyInit() or matchingInit() must be called before using this function.

void startDense ( )

inline

This function runs Edmonds' algorithm with a heuristic of postponing shrinks, therefore resulting in a faster algorithm for dense graphs.

Precondition

init(), greedyInit() or matchingInit() must be called before using this function.

void run ( )

inline

This function runs Edmonds' algorithm. An additional heuristic of postponing shrinks is used for relatively dense graphs (for which m>=2*n holds).

int matchingSize ( ) const

inline

This function returns the size (cardinality) of the current matching. After run() it returns the size of the maximum matching in the graph.

bool matching ( const Edge &  edge ) const

inline

This function returns true if the given edge is in the current matching.

Arc matching ( const Node &  n ) const

inline

This function returns the matching arc (or edge) incident to the given node in the current matching or INVALID if the node is not covered by the matching.

const MatchingMap& matchingMap ( ) const

inline

This function returns a const reference to a node map that stores the matching arc (or edge) incident to each node.

Node mate ( const Node &  n ) const

inline

This function returns the mate of the given node in the current matching or INVALID if the node is not covered by the matching.

Status status ( const Node &  n ) const

inline

This function returns the status of the given node in the Edmonds-Gallai decomposition.

const StatusMap& statusMap ( ) const

inline

This function returns a const reference to a node map that stores the status of each node in the Edmonds-Gallai decomposition.

bool barrier ( const Node &  n ) const

inline

This function returns true if the given node is in the barrier.