Module org.jgrapht.core
Package org.jgrapht.alg.matching.blossom.v5

Class KolmogorovWeightedMatching<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:
    MatchingAlgorithm<V,​E>
    public class KolmogorovWeightedMatching<V,​E>
extends java.lang.Object
implements MatchingAlgorithm<V,​E>
    This class computes weighted matchings in general graphs. Depending on the constructor parameter the weight of the resulting matching is maximized or minimized. If maximum of minimum weight perfect algorithm is needed, see KolmogorovWeightedPerfectMatching.

    This class reduces both maximum and minimum weight matching problems to the maximum and minimum weight perfect matching problems correspondingly. See KolmogorovWeightedPerfectMatching for relative definitions and algorithm description

    See Also:
    KolmogorovWeightedPerfectMatching

    • Field Detail

      • initialGraph

        private final Graph<V,​E> initialGraph
        The graph we are matching on

      • graph

        private Graph<V,​E> graph
        The graph created during the reduction

      • options

        private BlossomVOptions options
        BlossomVOptions used by the algorithm to match the problem instance

      • objectiveSense

        private ObjectiveSense objectiveSense
        The objective sense of the algorithm, i.e. whether to maximize or minimize the weight of the resulting matching

    • Constructor Detail

      • KolmogorovWeightedMatching

        public KolmogorovWeightedMatching​(Graph<V,​E> initialGraph)
        Constructs a new instance of the algorithm using the default options. The goal of the constructed algorithm is to minimize the weight of the resulting matching.
        Parameters:
        initialGraph - the graph for which to find a weighted matching

      • KolmogorovWeightedMatching

        public KolmogorovWeightedMatching​(Graph<V,​E> initialGraph,
                                  ObjectiveSense objectiveSense)
        Constructs a new instance of the algorithm using the default options. The goal of the constructed algorithm is to maximize or minimize the weight of the resulting matching depending on the maximize parameter.
        Parameters:
        initialGraph - the graph for which to find a weighted matching
        objectiveSense - objective sense of the algorithm

      • KolmogorovWeightedMatching

        public KolmogorovWeightedMatching​(Graph<V,​E> initialGraph,
                                  BlossomVOptions options)
        Constructs a new instance of the algorithm with the specified options. The goal of the constructed algorithm is to minimize the weight of the resulting matching.
        Parameters:
        initialGraph - the graph for which to find a weighted matching
        options - the options which define the strategies for the initialization and dual updates

      • KolmogorovWeightedMatching

        public KolmogorovWeightedMatching​(Graph<V,​E> initialGraph,
                                  BlossomVOptions options,
                                  ObjectiveSense objectiveSense)
        Constructs a new instance of the algorithm with the specified options. The goal of the constructed algorithm is to maximize or minimize the weight of the resulting matching depending on the maximize parameter.
        Parameters:
        initialGraph - the graph for which to find a weighted matching
        options - the options which define the strategies for the initialization and dual updates
        objectiveSense - objective sense of the algorithm

    • Method Detail

      • getMatching

        public MatchingAlgorithm.Matching<V,​E> getMatching()
        Computes and returns a matching of maximum or minimum weight in the initialGraph depending on the goal of the algorithm.
        Specified by:
        getMatching in interface MatchingAlgorithm<V,​E>
        Returns:
        weighted matching in the initialGraph

      • lazyComputeMaximumWeightMatching

        private void lazyComputeMaximumWeightMatching()
        Lazy computes optimal matching in the initialGraph by reducing the problem to the optimal perfect matching problem.

      • testOptimality

        public boolean testOptimality()
        Performs an optimality test after the perfect matching is computed. This test is done via KolmogorovWeightedPerfectMatching.testOptimality()

        More precisely, checks whether dual variables of all pseudonodes and resulting slacks of all edges are non-negative and that slacks of all matched edges are exactly 0. Since the algorithm uses floating point arithmetic, this check is done with precision of KolmogorovWeightedPerfectMatching.EPS

        In general, this method should always return true unless the algorithm implementation has a bug.

        Returns:
        true iff the assigned dual variables satisfy the dual linear program formulation AND complementary slackness conditions are also satisfied. The total error must not exceed EPS

      • getError

        public double getError()
        Computes the error in the solution to the dual linear program. This computation is done via KolmogorovWeightedPerfectMatching.getError(). More precisely, the total error equals the sum of:
        • Absolute value of edge slack if negative or the edge is matched
        • Absolute value of pseudonode variable if negative
        Returns:
        the total numeric error