My implementation of the Hungarian Algorithm
The Hungarian algorithm is a an algorithm used to solve a special type of linear programming problem known as an assignment problem. An assignment problem involves assigning n workers to m jobs to either minimize or maximize a cost. Typically these problems can be solved using the simplex method on an LP (O(2^N)). However, the Hungarian algorithm can be used to solve these problems considerably faster ( O(N^3) ). I learned about the algorithm last semester in a deterministic models class and have decided to try implementing it.
A more detialed description can be found here : http://www.math.harvard.edu/archive/20_spring_05/handouts/assignment_overheads.pdf
With my implementation of the algorithm, you can easily solve assignment problems in O(N^4) time as opposed to O(2^N) time. Simply import the class and use the static methods. The two main methods you will use are hungarian_algorithm and hungarian_minCost, although I have also made many of the helper methods public in case you want to use them for some reason. My implementation currently works for matrices of size mxn where m <= n. If you have a matrix of size m > n, simply take the transpose of the matrix before and after using the algorithm.