Class EdmondsKarpMFImpl<V,​E>

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

    public final class EdmondsKarpMFImpl<V,​E>
    extends MaximumFlowAlgorithmBase<V,​E>
    A flow network is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge can not exceed the capacity of the edge (note, that all capacities must be non-negative). A flow must satisfy the restriction that the amount of flow into a vertex equals the amount of flow out of it, except when it is a source, which "produces" flow, or sink, which "consumes" flow.

    This class computes maximum flow in a network using Edmonds-Karp algorithm. Be careful: for large networks this algorithm may consume significant amount of time (its upper-bound complexity is O(VE^2), where V - amount of vertices, E - amount of edges in the network).

    This class can also computes minimum s-t cuts. Effectively, to compute a minimum s-t cut, the implementation first computes a minimum s-t flow, after which a BFS is run on the residual graph.

    For more details see Andrew V. Goldberg's Combinatorial Optimization (Lecture Notes). Note: even though the algorithm accepts any kind of graph, currently only Simple directed and undirected graphs are supported (and tested!).

    • Constructor Detail

      • EdmondsKarpMFImpl

        public EdmondsKarpMFImpl​(Graph<V,​E> network)
        Constructs MaximumFlow instance to work with a copy of network. Current source and sink are set to null. If network is weighted, then capacities are weights, otherwise all capacities are equal to one. Doubles are compared using DEFAULT_EPSILON tolerance.
        Parameters:
        network - network, where maximum flow will be calculated
      • EdmondsKarpMFImpl

        public EdmondsKarpMFImpl​(Graph<V,​E> network,
                                 double epsilon)
        Constructs MaximumFlow instance to work with a copy of network. Current source and sink are set to null. If network is weighted, then capacities are weights, otherwise all capacities are equal to one.
        Parameters:
        network - network, where maximum flow will be calculated
        epsilon - tolerance for comparing doubles
    • Method Detail

      • getMaximumFlow

        public MaximumFlowAlgorithm.MaximumFlow<E> getMaximumFlow​(V source,
                                                                  V sink)
        Sets current source to source, current sink to sink, then calculates maximum flow from source to sink. Note, that source and sink must be vertices of the network passed to the constructor, and they must be different.
        Parameters:
        source - source vertex
        sink - sink vertex
        Returns:
        a maximum flow
      • calculateMaximumFlow

        public double calculateMaximumFlow​(V source,
                                           V sink)
        Sets current source to source, current sink to sink, then calculates maximum flow from source to sink. Note, that source and sink must be vertices of the network passed to the constructor, and they must be different. If desired, a flow map can be queried afterwards; this will not require a new invocation of the algorithm.
        Parameters:
        source - source vertex
        sink - sink vertex
        Returns:
        the value of the maximum flow
      • breadthFirstSearch

        private void breadthFirstSearch()
        Method which finds a path from source to sink the in the residual graph. Note that this method tries to find multiple paths at once. Once a single path has been discovered, no new nodes are added to the queue, but nodes which are already in the queue are fully explored. As such there's a chance that multiple paths are discovered.
      • augmentFlow

        private double augmentFlow()
        For all paths which end in the sink. trace them back to the source and push flow through them.
        Returns:
        total increase in flow from source to sink