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Munkres Assignment Algorithm

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Munkres Assignment Algorithm

by

Yi Cao (view profile)

 

17 Jun 2008 (Updated )

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

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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

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

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 ?
thanks

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14 Mar 2014 Markus Buehren

Markus Buehren (view profile)

There is another version of this package here: http://www.mathworks.com/matlabcentral/fileexchange/20652-hungarian-algorithm-for-linear-assignment-problems-v2-3

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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

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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

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20 Apr 2012 Arun Kumar Chithanar

This is much faster than the version 1.0. Thanks!

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30 Jan 2012 Max

Max (view profile)

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...

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01 Oct 2011 Christoph  
29 Sep 2011 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?

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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

Kevin Crosby (view profile)

Yi,

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

Thanks again!

Kevin

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24 Jun 2010 Yi Cao

Yi Cao (view profile)

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

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22 Jun 2010 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
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!

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  
Updates
23 Jun 2008

fix a bug

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