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https://github.com/mikolalysenko/push-relabel

A push-relabel network flow solver in JavaScript
https://github.com/mikolalysenko/push-relabel

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A push-relabel network flow solver in JavaScript

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README 

        
push-relabel

============

[Network flow](http://en.wikipedia.org/wiki/Flow_network) is a fundamental tool in computer science and operations research, and can be used to solve many common tasks such as:



* [Transportation problems](http://en.wikipedia.org/wiki/Transportation_problem)

* [Assignment problems](http://en.wikipedia.org/wiki/Assignment_problem)

* [Bipartite matching](http://en.wikipedia.org/wiki/Bipartite_matching#Maximum_bipartite_matchings)

* [Project selection](http://en.wikipedia.org/wiki/Max-flow_min-cut_theorem#Project_selection_problem)

* [Image segmentation](http://en.wikipedia.org/wiki/Graph_cuts_in_computer_vision)

* [Stereo vision](http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1315016&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1315016)



This library is an implementation of Goldberg and Tarjan's [push-relabel algorithm](http://en.wikipedia.org/wiki/Push%E2%80%93relabel_maximum_flow_algorithm) for solving network flow problems in JavaScript.  It use relabel-to-front ordering as well as the global and gap relabelling heuristics, as described by [Cherkassy and Goldberg](https://www.ads.tuwien.ac.at/teaching/archiv/praktika/CherkasskyGoldberg-1995-MaxFlow.pdf), giving it a run time on the order of |V|^3 in the worst case.



Currently in early development, patches welcome!



Usage

=====

To install the library, use npm:



    npm install push-relabel

    

And then you can call it as follows:



```javascript

//Solve flow for following network:

//

//       1

//      ^ |

//   2 /  |1

//    /   V   1

//  s=0-->2--->3

//      9 |    |

//        |7   |7

//        V    V

//        4--->t=5

//            4

//

var num_vertices = 6

var source       = 0

var sink         = 5

var edges        = [[0,1],[0,2],[1,2],[2,3],[2,4],[3,5],[4,5]]

var capacities   = [   2,   9,    1,    1,    7,    7,    4  ]



//Load library

var pushRelabel = require("push-relabel")



//Compute maximum flow

var flow = pushRelabel.maxFlow(num_vertices, source, sink, edges, capacities)

for(var i=0; i= `edges.length`

* `flow` (optional) is an array which will get the resulting flow.  If not specified, a new flow array is allocated.  Must be of size at least `edges.length`

* `dual` (optional) is the topological dual of the flow network.  If not specified, a new dual is computed.



**WARNING** If you don't specify a dual, the library will permute the order of the edges/capacities array



Returns: The flow, which is stored in the object `flow`



### `pushRelabel.minCut(num_vertices, source, sink, edges, capacities[, cut, dual])`

Computes a [minimum cut](http://en.wikipedia.org/wiki/Minimum_cut) in a flow network



* `num_vertices` is the number of vertices in the graph

* `source` is the index of the source vertex

* `sink` is the index of the sink vertex

* `edges` is a list of edges in the graph

* `capacities` is a list of per-edge capacities.  Must have size >= `edges.length`

* `cut` (optional) is an array which will get the resulting cut.  If not specified, a new uint8 array is allocated.  Must be of size at least `num_vertices

* `dual` (optional) is the topological dual of the flow network.  If not specified, a new dual is computed.



**WARNING** If you don't specify a dual, the library will permute the order of the edges/capacities array



Returns: The cut



Credits

=======

(c) 2013 Mikola Lysenko.  BSD License