max flow

Author: chen0040

README.md

@@ -484,4 +484,40 @@ for(var v = 1; v < g.V; ++v){
         console.log('=====distance: '  + bf.distanceTo(v) + '=========');
     }
 }
+```
+
+### Find the MaxFlow-MinCut using Ford-Fulkerson algorithm
+
+The sample code below show how to obtain the MaxFlow-MinCut of a directed weighted graph using ford-fulkerson algorithm:
+
+```javascript
+var jsgraphs = require('js-graph-algorithms');
+var g = new jsgraphs.FlowNetwork(8);
+g.addEdge(new jsgraphs.FlowEdge(0, 1, 10));
+g.addEdge(new jsgraphs.FlowEdge(0, 2, 5));
+g.addEdge(new jsgraphs.FlowEdge(0, 3, 15));
+g.addEdge(new jsgraphs.FlowEdge(1, 4, 9));
+g.addEdge(new jsgraphs.FlowEdge(1, 5, 15));
+g.addEdge(new jsgraphs.FlowEdge(1, 2, 4));
+g.addEdge(new jsgraphs.FlowEdge(2, 5, 8));
+g.addEdge(new jsgraphs.FlowEdge(2, 3, 4));
+g.addEdge(new jsgraphs.FlowEdge(3, 6, 16));
+g.addEdge(new jsgraphs.FlowEdge(4, 5, 15));
+g.addEdge(new jsgraphs.FlowEdge(4, 7, 10));
+g.addEdge(new jsgraphs.FlowEdge(5, 7, 10));
+g.addEdge(new jsgraphs.FlowEdge(5, 6, 15));
+g.addEdge(new jsgraphs.FlowEdge(6, 2, 6));
+g.addEdge(new jsgraphs.FlowEdge(6, 7, 10)); 
+
+var source = 0;
+var target = 7;
+var ff = new jsgraphs.FordFulkerson(g, source, target);
+console.log('max-flow: ' + ff.value);
+
+var minCut = ff.minCut(g);
+
+for(var i = 0; i < minCut.length; ++i) {
+    var e = minCut[i];
+    console.log('min-cut: (' + e.from() + ", " + e.to() + ')');
+}
 ```

package.json

@@ -1,6 +1,6 @@
 {
   "name": "js-graph-algorithms",
-  "version": "1.0.8",
+  "version": "1.0.9",
   "description": "Package implements data structures and algorithms for processing various types of graphs",
   "author": "Xianshun Chen",
   "contributors": [

src/jsgraphs.js

@@ -1043,7 +1043,7 @@ var jsgraphs = jsgraphs || {};
     var FordFulkerson = function(G, s, t) {
         this.value = 0;
         var V = G.V;
-        var bottle = Numbers.MAX_VALUE;
+        var bottle = Number.MAX_VALUE;
         this.marked = null;
         this.edgeTo = null;
         this.s = s;
@@ -1058,6 +1058,7 @@ var jsgraphs = jsgraphs || {};
                 this.edgeTo[x].addResidualFlowTo(x, bottle);
             }
 
+            
             this.value += bottle;
         }
     };
@@ -1072,28 +1073,48 @@ var jsgraphs = jsgraphs || {};
         }
 
         var queue = new jss.Queue();
-        queue.push(this.s);
+        queue.enqueue(this.s);
 
+        this.marked[this.s] = true;
         while(!queue.isEmpty()){
             var v = queue.dequeue();
             var adj_v = G.adj(v);
-            this.marked[v] = true;
+            
             for (var i = 0; i < adj_v.length; ++i) {
                 var e = adj_v[i];
                 var w = e.other(v);
-                if(e.residualCapacityTo(v) > 0){
+                if(!this.marked[w] && e.residualCapacityTo(w) > 0){
+                    this.edgeTo[w] = e;
+                    this.marked[w] = true;
                     if(w == this.t){
                         return true;
                     }
-                    this.edgeTo[w] = e;
-                    queue.push(w);
+                    
+                    queue.enqueue(w);
                 }
             }
         }
 
         return false;
     };
+    
+    FordFulkerson.prototype.minCut = function(G) {
+        var cuts = [];
+        var V = G.V;
+        for(var v = 0; v < V; ++v){
+            var adj_v = G.adj(v);
+            for(var i = 0; i < adj_v.length; ++i) {
+                var e = adj_v[i];
+                if(e.from() == v && e.residualCapacityTo(e.other(v)) == 0) {
+                    cuts.push(e);
+                }
+            }
+        }
+        
+        return cuts;
+    };
 
+    jss.FordFulkerson = FordFulkerson;
 })(jsgraphs);
 
 if(module) {

test/ford-fulkerson-spec.js

@@ -0,0 +1,37 @@
+var expect = require('chai').expect;
+var jsgraphs = require('../src/jsgraphs');
+
+describe('MaxFlow-MinCut', function(){
+   it('should work', function(){
+        var g = new jsgraphs.FlowNetwork(8);
+        g.addEdge(new jsgraphs.FlowEdge(0, 1, 10));
+        g.addEdge(new jsgraphs.FlowEdge(0, 2, 5));
+        g.addEdge(new jsgraphs.FlowEdge(0, 3, 15));
+        g.addEdge(new jsgraphs.FlowEdge(1, 4, 9));
+        g.addEdge(new jsgraphs.FlowEdge(1, 5, 15));
+        g.addEdge(new jsgraphs.FlowEdge(1, 2, 4));
+        g.addEdge(new jsgraphs.FlowEdge(2, 5, 8));
+        g.addEdge(new jsgraphs.FlowEdge(2, 3, 4));
+        g.addEdge(new jsgraphs.FlowEdge(3, 6, 16));
+        g.addEdge(new jsgraphs.FlowEdge(4, 5, 15));
+        g.addEdge(new jsgraphs.FlowEdge(4, 7, 10));
+        g.addEdge(new jsgraphs.FlowEdge(5, 7, 10));
+        g.addEdge(new jsgraphs.FlowEdge(5, 6, 15));
+        g.addEdge(new jsgraphs.FlowEdge(6, 2, 6));
+        g.addEdge(new jsgraphs.FlowEdge(6, 7, 10)); 
+       
+        var source = 0;
+        var target = 7;
+        var ff = new jsgraphs.FordFulkerson(g, source, target);
+        console.log('max-flow: ' + ff.value);
+        expect(ff.value).to.equal(28);
+       
+        var minCut = ff.minCut(g);
+       
+        for(var i = 0; i < minCut.length; ++i) {
+            var e = minCut[i];
+            console.log('min-cut: (' + e.from() + ", " + e.to() + ')');
+        }
+        
+   });
+});