Yes this is classicalproblem,
it can be reduced to Min-cost max-flow. But there are other algorithms. you
can find answer here
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=hungarianAlgorithm

http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=minimumCostFlow1

2009/3/19, libicocco <libico...@gmail.com>:
>
>
> Dear All,
>
> I have a problem which i'm sure more people have think about before,
> but i can't find any solution around.
> I want to select 1 element per row and 1 element per column in a
> matrix, and that this set of elements has minimum sum. The application
> is, for example, matching of features: given a distance matrix, i want
> the matches (pairs of features) that give me minimum sum of distances.
>
> Any idea?
>
> PS.- the matrices can be non-square; in that case there will be one
> dimension not completely covered with the matches.
>
> >
>

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