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Munkres Assignment Algorithm


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Munkres Assignment Algorithm



17 Jun 2008 (Updated )

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.


Assignprob.Zip, Functions For The Rectangular Assignment Problem, and Hungarian Algorithm inspired this file.

This file inspired K Best Assignment Algorithm and Lapjv Jonker Volgenant Algorithm For Linear Assignment Problem V3.0.

MATLAB release MATLAB 7.6 (R2008a)
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Comments and Ratings (14)
31 Oct 2014 Matteo

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 ?

14 Mar 2014 Markus Buehren

There is another version of this package here:

09 Oct 2012 David Manegold

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

08 Oct 2012 David Manegold

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

can I send you the matrix

20 Apr 2012 Arun Kumar Chithanar

This is much faster than the version 1.0. Thanks!

30 Jan 2012 Max


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

01 Oct 2011 Christoph  
29 Sep 2011 Christoph


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?

12 Oct 2010 Jiangmin zhang

but i have a question

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

30 Jun 2010 Kevin Crosby


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

Thanks again!


24 Jun 2010 Yi Cao


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.


22 Jun 2010 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

My distance matrix is found here:

Do you have a quick fix for this?


03 Mar 2010 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.

05 Apr 2009 V. Poor  
23 Jun 2008

fix a bug

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