Class HopcroftKarpMaximumCardinalityBipartiteMatching<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:

    public class HopcroftKarpMaximumCardinalityBipartiteMatching<V,​E>
    extends java.lang.Object
    implements MatchingAlgorithm<V,​E>
    Implementation of the well-known Hopcroft Karp algorithm to compute a matching of maximum cardinality in a bipartite graph. The algorithm runs in $O(|E| \cdot \sqrt{|V|})$ time. This implementation accepts undirected graphs which may contain self-loops and multiple edges. To compute a maximum cardinality matching in general (non-bipartite) graphs, use SparseEdmondsMaximumCardinalityMatching instead.

    The Hopcroft Karp matching algorithm computes augmenting paths of increasing length, until no augmenting path exists in the graph. At each iteration, the algorithm runs a Breadth First Search from the exposed (free) vertices, until an augmenting path is found. Next, a Depth First Search is performed to find all (vertex disjoint) augmenting paths of the same length. The matching is augmented along all discovered augmenting paths simultaneously.

    The original algorithm is described in: Hopcroft, John E.; Karp, Richard M. (1973), "An n5/2 algorithm for maximum matchings in bipartite graphs", SIAM Journal on Computing 2 (4): 225–231, doi:10.1137/0202019 A coarse overview of the algorithm is given in:

    Joris Kinable
    • Constructor Detail

      • HopcroftKarpMaximumCardinalityBipartiteMatching

        public HopcroftKarpMaximumCardinalityBipartiteMatching​(Graph<V,​E> graph,
                                                               java.util.Set<V> partition1,
                                                               java.util.Set<V> partition2)
        Constructs a new instance of the Hopcroft Karp bipartite matching algorithm. The input graph must be bipartite. For efficiency reasons, this class does not check whether the input graph is bipartite. Invoking this class on a non-bipartite graph results in undefined behavior. To test whether a graph is bipartite, use GraphTests.isBipartite(Graph).
        graph - bipartite graph
        partition1 - the first partition of vertices in the bipartite graph
        partition2 - the second partition of vertices in the bipartite graph