Matching (JGAlgo - Core 0.1.1.2 API)

```
public interface Matching
```
A matching in a graph.
Given a graph \(G=(V,E)\), a matching is a sub set of edges \(M\) such that any vertex in \(V\) has at most one adjacent edge in \(M\). Its a common problem to compute the maximum (cardinality) matching, namely the matching with the greatest number of edges. Another variant is to compute the maximum weighted matching with respect to some weight function.

Author:

Barak Ugav

See Also:

MaximumMatching, MaximumMatchingWeighted, Wikipedia

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`boolean`	`containsEdge(int edge)`	Check whether an edge is part of the matching.
`it.unimi.dsi.fastutil.ints.IntCollection`	`edges()`	The collection of edges forming this matching.
`boolean`	`isVertexMatched(int vertex)`	Check whether a vertex is matched by the matching.
`double`	`weight(WeightFunction w)`	Get the weight of the matching with respect to some weight function.

- Method Detail
  - isVertexMatched
```
boolean isVertexMatched(int vertex)
```
    Check whether a vertex is matched by the matching.
    A vertex \(v\) is said to be matched if the matching contains an edge \((v,w)\) for some other vertex \(w\).
    
    Parameters:
    
    vertex - a vertex
    
    Returns:
    
    true if vertex has an adjacent edge in the matching, else false
  - containsEdge
```
boolean containsEdge(int edge)
```
    Check whether an edge is part of the matching.
    A matching \(M\) is a sub set of \(E\), the edge set of the graph. This method check whether a given edge is in \(M\).
    
    Parameters:
    
    edge - an edge
    
    Returns:
    
    true if the edge is part of the matching, else false
  - edges
```
it.unimi.dsi.fastutil.ints.IntCollection edges()
```
    The collection of edges forming this matching.
    
    Returns:
    
    collection containing all the edges that are part of this matching
  - weight
```
double weight(WeightFunction w)
```
    Get the weight of the matching with respect to some weight function.
    The weight of a matching is defined as the sum of its edges weights.
    
    Parameters:
    
    w - an edge weight function
    
    Returns:
    
    the sum of this matching edges weights