Ford-Fulkerson Algorithm for Maximum Flow Problem
When a Graph Represent a Flow Network where every edge has a capacity. Also given that two vertices, source 's' and sink 't' in the graph, we can find the maximum possible flow from s to t with having following constraints:
- Flow on an edge doesn't exceed the given edge capacity
- Incoming flow is equal to Outgoing flow for every vertex excluding sink and source
- Start with f(e) = 0 for all edge e ∈ E.
- Find an augmenting path P in the residual graph Gf .
- Augment flow along path P.
- Repeat until you get stuck.
Consider the following graph
Maximum possible flow in the given graph is 23
var fordFulkerson = require('graph-theory-ford-fulkerson'); var graph = [ [ 0, 16, 13, 0, 0, 0 ], [ 0, 0, 10, 12, 0, 0 ], [ 0, 4, 0, 0, 14, 0 ], [ 0, 0, 9, 0, 0, 20 ], [ 0, 0, 0, 7, 0, 4 ], [ 0, 0, 0, 0, 0, 0 ] ]; console.log("The maximum possible flow is " + fordFulkerson(graph, 0, 5));
require('graph-theory-ford-fulkerson')( graph, source, sink )
Compute the maximum flow in a flow network between source node
source and sink node
graph: The Graph which representing the flow network
source: source vertex
sink: sink vertex
Returns: Returns a number representing the maximum flow.
npm install graph-theory-ford-fulkerson
© 2016 Prabod Rathnayaka. MIT License.