Class MaximumWeightBipartiteMatching<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:
    MatchingAlgorithm<V,​E>

    public class MaximumWeightBipartiteMatching<V,​E>
    extends Object
    implements MatchingAlgorithm<V,​E>
    Maximum weight matching in bipartite graphs.

    Running time is $O(n(m+n \log n))$ where n is the number of vertices and m the number of edges of the input graph. Uses exact arithmetic and produces a certificate of optimality in the form of a tight vertex potential function.

    This is the algorithm and implementation described in the LEDA book. See the LEDA Platform of Combinatorial and Geometric Computing, Cambridge University Press, 1999.

    Author:
    Dimitrios Michail
    • Constructor Detail

      • MaximumWeightBipartiteMatching

        public MaximumWeightBipartiteMatching​(Graph<V,​E> graph,
                                              Set<V> partition1,
                                              Set<V> partition2)
        Constructor.
        Parameters:
        graph - the input graph
        partition1 - the first partition of the vertex set
        partition2 - the second partition of the vertex set
        Throws:
        IllegalArgumentException - if the graph is not undirected
      • MaximumWeightBipartiteMatching

        public MaximumWeightBipartiteMatching​(Graph<V,​E> graph,
                                              Set<V> partition1,
                                              Set<V> partition2,
                                              Function<Comparator<BigDecimal>,​org.jheaps.AddressableHeap<BigDecimal,​V>> heapSupplier)
        Constructor.
        Parameters:
        graph - the input graph
        partition1 - the first partition of the vertex set
        partition2 - the second partition of the vertex set
        heapSupplier - a supplier for the addressable heap to use in the algorithm.
        Throws:
        IllegalArgumentException - if the graph is not undirected
    • Method Detail

      • getPotentials

        public Map<V,​BigDecimal> getPotentials()
        Get the vertex potentials.

        This is a tight non-negative potential function which proves the optimality of the maximum weight matching. See any standard textbook about linear programming duality.

        Returns:
        the vertex potentials
      • getMatchingWeight

        public BigDecimal getMatchingWeight()
        Get the weight of the matching.
        Returns:
        the weight of the matching