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PHP implementation of various algorithms for the Linear Assignment Problem.
Documentation
The original paper by Jonker and Volgenant can be found SpringerLink or in the folder.
Usage
The hungarian library contains the fundamentals needed to solve a linear assignment problem, as well as some abstractions to make integration easier.
Basic usage
The plain matrix object is indexed by integer and allows getting and setting of values, it is always a square matrix.
To fill a three by three matrix, you might do the following.
Using the matrix above, we can use the Hungarian method.
Or, if you'd want to find the highest scoring assignment, you can call use solveMax().
Under the hood, this is equivalent to solving the matrix after calling invert().
This result can then be used as a list of tuples.
Alternate types of matrices
In most cases, you're not actually trying to pair integers, instead you might want to assign users to tasks. One way to do this, is by using string labels
Another option is by using objects as labels, for example using Eloquent
MatrixBuilder
Finally, it is likely you don't have a square matrix or need to write quite some boilerplate code to create a proper matrix. To help in this, you can use the MatrixBuilder class.
This will automatically ensure your matrix is square, augmenting it where needed.
If desired, you can easily remove unassigned rows and columns from the results
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