如何使用 JUNG 的 Edmonds Karp 获得每个可能的源/汇节点对的最大流量？

Posted 2023-02-19

【中文标题】如何使用 JUNG 的 Edmonds Karp 获得每个可能的源/汇节点对的最大流量？

【英文标题】：How to get max flow for every possible source/sink node pair using JUNG's Edmonds Karp?

【发布时间】：2020-08-03 09:55:40

【问题描述】：

我有一些简单的 Java/JUNG 代码来创建有向图，添加一些带有权重和容量值的边，并运行从源节点到汇节点的最大流量分析。

如果你有：A --- (容量 2) -----> B ---- (容量 5)----> C 并且想从 A->C 中找到最大流量，它会是 2。

import edu.uci.ics.jung.algorithms.flows.EdmondsKarpMaxFlow;
import edu.uci.ics.jung.graph.DirectedSparseMultigraph;
import edu.uci.ics.jung.graph.util.EdgeType;
import org.apache.commons.collections15.Factory;
import org.apache.commons.collections15.Transformer;

import java.util.HashMap;
import java.util.Map;

public class stack 
    static int edgeCount = 0;

    static class MyNode 
        int id;
        public MyNode(int id) 
            this.id = id;
        
        public String toString() 
            return "V"+id;
        
    

    static class MyLink 

        double capacity;
        double weight;
        int id;

        public MyLink(double weight, double capacity) 
            this.id = edgeCount++;
            this.weight = weight;
            this.capacity = capacity;
        
        public String toString() 
            return "E"+id;
        

    
    public static void main(String[] args)
        DirectedSparseMultigraph<MyNode, MyLink> g = new DirectedSparseMultigraph<MyNode, MyLink>();

        Transformer<MyLink, Double> capTransformer = new Transformer<MyLink, Double>()
            public Double transform(MyLink link) 
                return link.capacity;
            
        ;

        Map<MyLink, Double> edgeFlowMap = new HashMap<MyLink, Double>();
        // This Factory produces new edges for use by the algorithm
        Factory<MyLink> edgeFactory = new Factory<MyLink>() 
            public MyLink create() 
                return new MyLink(1.0, 1.0);
            
        ;

        // Create some MyNode objects to use as vertices
        MyNode n1 = new MyNode(1);
        MyNode n2 = new MyNode(2);
        MyNode n3 = new MyNode(3);
        MyNode n4 = new MyNode(4);
        MyNode n5 = new MyNode(5);
        MyNode n6 = new MyNode(6);
        MyNode n7 = new MyNode(7);
        // Add some directed edges along with the vertices to the graph
        g.addEdge(new MyLink(2.0, 48),n1, n2, EdgeType.DIRECTED);
        g.addEdge(new MyLink(2.0, 58),n2, n3, EdgeType.DIRECTED);
        g.addEdge(new MyLink(3.0, 192), n3, n5, EdgeType.DIRECTED);
        g.addEdge(new MyLink(2.0, 48), n5, n4, EdgeType.DIRECTED);
        g.addEdge(new MyLink(2.0, 20), n6, n1, EdgeType.DIRECTED);
        g.addEdge(new MyLink(8, 24), n7, n4, EdgeType.DIRECTED);

        System.out.println("RUNNING EDMONDS KARP MAX FLOW FOR SOURCE " + n1.toString() + " TO SINK " + n2.toString());
        EdmondsKarpMaxFlow<MyNode, MyLink> edk = new EdmondsKarpMaxFlow(g, n1, n2, capTransformer, edgeFlowMap, edgeFactory);
        edk.evaluate();
        System.out.println("The max flow is: " + edk.getMaxFlow());
    

运行会输出：

运行 EDMONDS KARP MAX FLOW FOR SOURCE V1 TO SINK V2 最大流量 是：48

如何编写算法以使其在每对可能的源和汇上运行，以便我可以看到图中所有路径的最大流量？对这些东西完全陌生，所以任何东西都有帮助！

【参考方案1】：

只需为每对节点运行算法。没有已知算法对有向图更有效：All pair Maximum Flow