Interface MinimumCostFlowProblem<V,E>

Type Parameters:
V - the graph vertex type
E - the graph edge type
All Known Implementing Classes:
MinimumCostFlowProblem.MinimumCostFlowProblemImpl
public interface MinimumCostFlowProblem<V,E>
This class represents a minimum cost flow problem. It serves as input for the minimum cost flow algorithms.

The minimum cost flow problem is defined as follows: \[ \begin{align} \mbox{minimize}~& \sum_{e\in \delta^+(s)}c_e\cdot f_e &\\ \mbox{s.t. }&\sum_{e\in \delta^-(i)} f_e - \sum_{e\in \delta^+(i)} f_e = b_e & \forall i\in V\\ &l_e\leq f_e \leq u_e & \forall e\in E \end{align} \] Here $\delta^+(i)$ and $\delta^-(i)$ denote the outgoing and incoming edges of vertex $i$ respectively. The parameters $c_{e}$ define a cost for each unit of flow on the arc $e$, $l_{e}$ define minimum arc flow and $u_{e}$ define maximum arc flow.

See Also:

  • Method Details

    • getGraph

      Graph<V,E> getGraph()
      Returns the flow network
      Returns:
      the flow network

    • getNodeSupply

      Function<V,Integer> getNodeSupply()
      Returns a function which defines the supply and demand of each node in that network. Supplies can be positive, negative or 0. Nodes with positive negative supply are the demand nodes, nodes with zero supply are the transhipment nodes. Flow is always directed from nodes with positive supply to nodes with negative supply. Summed over all nodes, the total demand should equal 0.
      Returns:
      supply function

    • getArcCapacityLowerBounds

      Function<E,Integer> getArcCapacityLowerBounds()
      Returns a function which specifies the minimum capacity of an arc. The minimum capacity is the minimum amount of flow that has to go through an arc.
      Returns:
      arc capacity lower bounding function

    • getArcCapacityUpperBounds

      Function<E,Integer> getArcCapacityUpperBounds()
      Returns a function which specifies the maximum capacity of an arc. The flow through an arc cannot exceed this upper bound.
      Returns:
      arc capacity upper bounding function

    • getArcCosts

      Function<E,Double> getArcCosts()
      Returns a function which specifies the network arc costs. Every unit of flow through an arc will have the price of the cost of this arc.
      Returns:
      arc cost function