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Munkres Assignment Algorithm

version 1.0 (2.69 KB) by

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

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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.

Comments and Ratings (18)

yechen tang

Hello, Yi Cao

Thank you for uploading Munkres algorithm. However, as this assignment is only for Minimum assignment, If i want to assign for Maximum assignment then what changes needs to be done in your code?

Suppose matrix [2, 4, 6;8, 6, 10;12, 14, 20]

Min. Assignment is 24. But If I want to Max. assignment then?

Thank you in Advance.

mathu Mari

Is it possible for you explain the commands how it is perform here? Need to understand whole program. I m new to matlab and programming.

Paul Quinn

Bug: fails for input row vector [5 4 3 1].
Fix(?): validCol = any(validMat, 1); (dimension for any is not specified in the original code for validCol.)


Matteo (view profile)

Hi people,
I a question about the hungarian algorithm. this algorithm is optimal algorithm for the assignment problem, and the time complexity is O(n^3), right?
But , if the input is the multidimensional matrix, it's possible to use the hungarian algorithm? how does it change the algorithm and the time complexity ?

there is no solution for the following matrix?
1 4 Inf
Inf Inf 5
Inf Inf 7
How do I modify such that it provides the
assignment =
1 0 0
0 0 1
0 0 0

I have a 15x51 matrix on which this algorithm fails. the JV handles it.

can I send you the matrix

This is much faster than the version 1.0. Thanks!


Max (view profile)


i have also a cost matrix which returns zero assignments while the Hungarian ( algorithm works fine...




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?

but i have a question

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

Kevin Crosby

Kevin Crosby (view profile)


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

Thanks again!


Yi Cao

Yi Cao (view profile)


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.


Kevin Crosby

Kevin Crosby (view profile)

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

My distance matrix is found here:

Do you have a quick fix for this?


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

V. Poor


fix a bug

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MATLAB 7.6 (R2008a)

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