Munkres Assignment Algorithm

An efficient implementation of the Munkres algorithm for the assignment problem.

Description

Munkres algorithm (also known as Hungarian algorithm) is an efficient algorithm to solve the assignment problem in polynomial-time. The algorithm has many applications in combinatorial optimization, for example in Traveling Salesman problem.

There are a few submissions in the File Exchange for the Munkres algorithm. However, most of them are not efficient. Therefore, I decided to develop my own code. By comparing with existing programms, this code is about two to 5 times faster. For instance, for a 400 x 400 random example, this code can solve it in 4 to 6 seconds, whilst other programs have to take about 17 to 35 seconds.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
assignprob.zip, Functions for the rectangular assignment problem, Hungarian Algorithm
This submission has inspired the following:
LAPJV - Jonker-Volgenant Algorithm for Linear Assignment Problem V2.4, K-Best Assignment Algorithm

• MATLAB release: MATLAB 7.6 (R2008a)

[V. Poor]

 

[Zacharias Voulgaris]

Truly excellent. It has everything you could ask of a Matlab program: good structure, excellent comments, simplicity, flow and efficiency. Thank you for sharing.

[Kevin Crosby]

This is extremely fast compared to the other Hungarian algorithms I've seen posted here.

I have successfully used this many times to optimally connect line segments such that the total cost is minimized.

However, I did find a case in which the assignment matrix does not return any matches, but some of the slower algorithms do.

For example, i got results using Markus Buehren's algorithm at
http://www.mathworks.com/matlabcentral/fileexchange/6543

My distance matrix is found here:
http://www.bigfoot.com/~Kevin.Crosby/public/distance.mat

Do you have a quick fix for this?

Thanks!

[Yi Cao]

Kevin,

Thanks for comments. I have looked at your problem. Actually, the problem does not have a valid solution. The code you linked does not provide a valid solution either. If you check the solution, you will find many zeros, which means no valid assignment can be done for these positions.

HTH
Yi

[Kevin Crosby]

Yi,

There was a problem with my data, that did not occur in any of my other cases.

Thanks again!

Kevin

[Jiangmin zhang]

but i have a question

is the time complexity of your algorithm on the order of n^3 or n^4?

[Christoph]

Hi

I have a cost matrix for which this script does not seem to work. It seems to make random assignments where the candidate has maximum costs (inf). Could you help?

[Christoph]

 

[Max]

Hi,

i have also a cost matrix which returns zero assignments while the Hungarian (http://www.mathworks.com/matlabcentral/fileexchange/11609-hungarian-algorithm) algorithm works fine...