NAME

Algorithm::Kuhn::Munkres - Determines the maximum weight perfect matching in a weighted complete bipartite graph

VERSION

This document describes Algorithm::Kuhn::Munkres version 1.0.7

SYNOPSIS

    use Algorithm::Kuhn::Munkres qw( assign );
    my @matrix = ([1,2,3,4],[2,4,6,8],[3,6,9,12],[4,8,12,16]);
    my ($cost,$mapping) = assign(@matrix);
 
  

DESCRIPTION

    Implementation of the Kuhn-Munkres algorithm. The algorithm finds the maximum weight
    perfect matching in a weighted complete bipartite graph. This problem is also known as 
    the "Assignment Problem".

INTERFACE

max_weight_perfect_matching

Determines the maximum weight perfect matching in a weighted complete bipartite graph. The single argument is a matrix representing the weights of the edges in the bipartite graph. The matrix must be implemented as a list of array objects. The output is a tuple consisting of the total weight (cost) of the perfect matching, and a reference to a hash representing edges in the mapping.

    use Algorithm::Kuhn::Munkres qw( assign );
    my @matrix = ([1,2,3,4],[2,4,6,8],[3,6,9,12],[4,8,12,16]);
    my ($cost,$mapping) = assign(@matrix);
    

assign

Synonym for max_weight_perfect_matching

DIAGNOSTICS

    Ideally, I would list every single error and warning message that the module can
    generate (even the ones that will "never happen"), with a full
    explanation of each problem, one or more likely causes, and any
    suggested remedies. I'm not that good a person right now.

CONFIGURATION AND ENVIRONMENT

Algorithm::Kuhn::Munkres requires no configuration files or environment variables.

DEPENDENCIES

List::Util

INCOMPATIBILITIES

None reported.

BUGS AND LIMITATIONS

No bugs have been reported.

Please report any bugs or feature requests to bug-algorithm-kuhn-munkres@rt.cpan.org, or through the web interface at http://rt.cpan.org.

AUTHOR

Martin-Louis Bright <mlbright@gmail.com>

ACKNOWLEDGEMENTS

This implementation is a translation of the python code at http://www.enseignement.polytechnique.fr/informatique/INF441/INF441b/code/kuhnMunkres.py

To understand the algorithm, the following web resources were invaluable: (http://www.cse.ust.hk/~golin/COMP572/Notes/Matching.pdf), (http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=hungarianAlgorithm), (http://www.math.uwo.ca/~mdawes/courses/344/kuhn-munkres.pdf)

LICENCE AND COPYRIGHT

Copyright (c) 2010, Martin-Louis Bright <mlbright@gmail.com>. All rights reserved.

This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself. See perlartistic.

DISCLAIMER OF WARRANTY

BECAUSE THIS SOFTWARE IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE SOFTWARE, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE SOFTWARE "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE SOFTWARE IS WITH YOU. SHOULD THE SOFTWARE PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR, OR CORRECTION.

IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE SOFTWARE AS PERMITTED BY THE ABOVE LICENCE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE SOFTWARE TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

cpanm Algorithm::Kuhn::Munkres

perl -MCPAN -e shell
install Algorithm::Kuhn::Munkres