Interface BipartiteMatchingProblem<V,E>

Type Parameters:
V - the graph vertex types
E - the graph edge type
All Known Implementing Classes:
BipartiteMatchingProblem.BipartiteMatchingProblemImpl
public interface BipartiteMatchingProblem<V,E>
This class represents a bipartite matching problem. The problem can be weighted or unweighted depending on the isWeighted().

The minimum weight (minimum cost) perfect bipartite matching problem is defined as follows: \[ \begin{align} \mbox{minimize}~& \sum_{e \in E}c_e\cdot x_e &\\ \mbox{s.t. }&\sum_{e\in \delta(v)} x_e = 1 & \forall v\in V\\ &x_e \in \{0,1\} & \forall e\in E \end{align} \] Here $\delta(v)$ denotes the set of edges incident to the vertex $v$. The parameters $c_{e}$ define a cost of adding the edge $e$ to the matching. If the problem is unweighted, the values $c_e$ are equal to 1 in the problem formulation.

This class can define bipartite matching problems without the requirement that every edge must be matched, i.e. non-perfect matching problems. These problems are called maximum cardinality bipartite matching problems. The goal of the maximum cardinality matching problem is to find a matching with maximum number of edges. If the cost function is used in this setup, the goal is to find the cheapest matching among all matchings of maximum cardinality.

See Also:

  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Interface
    Description
    static class 
    BipartiteMatchingProblem.BipartiteMatchingProblemImpl<V,E>
    Default implementation of a Bipartite Matching Problem

  • Method Summary

    Modifier and Type
    Method
    Description
    default void
    dumpCosts()
    Dumps the problem edge costs to the underlying graph.
    Function<E,Double>
    getCosts()
    Returns a cost function of this problem.
    Graph<V,E>
    getGraph()
    Returns the graph, which defines the problem
    Set<V>
    getPartition1()
    Returns one of the 2 partitions of the graph (no 2 vertices in this set share an edge)
    Set<V>
    getPartition2()
    Returns one of the 2 partitions of the graph (no 2 vertices in this set share an edge)
    boolean
    isWeighted()
    Determines if this problem is weighted or not.

  • Method Details

    • getGraph

      Graph<V,E> getGraph()
      Returns the graph, which defines the problem
      Returns:
      the graph, which defines the problem

    • getPartition1

      Set<V> getPartition1()
      Returns one of the 2 partitions of the graph (no 2 vertices in this set share an edge)
      Returns:
      one of the 2 partitions of the graph

    • getPartition2

      Set<V> getPartition2()
      Returns one of the 2 partitions of the graph (no 2 vertices in this set share an edge)
      Returns:
      one of the 2 partitions of the graph

    • getCosts

      Function<E,Double> getCosts()
      Returns a cost function of this problem. This function must be defined for all edges of the graph. In the case the problem is unweighted, the function must return any constant value for all edges.
      Returns:
      a cost function of this problem

    • isWeighted

      boolean isWeighted()
      Determines if this problem is weighted or not.
      Returns:
      true is the problem is weighted, false otherwise

    • dumpCosts

      default void dumpCosts()
      Dumps the problem edge costs to the underlying graph.