Hungarian method

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Whinii F.
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Posts: 151
Joined: Wed Aug 21, 2002 12:07 am
Location: Seoul, Korea

Hungarian method

Post by Whinii F. »

Anyone could point out some useful reference or papers to the hungarian method? I tried google and citeseer, and acm portal but I could pick out which is the one I need.

And one more: Are there more than one implementations which are called hungarian methods? I found two differing implementation and they both are called as hungarian. I'm really confused.

Thanks in advance!!! :)
JongMan @ Yonsei

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Location: Wejherowo

Post by makbet »

hungarian method is generally for finding perfect matchings in bipartite graphs.
Given a semi-matched graph, you find an augmenting path, that is, a path that starts and ends with an unmatched vertice, and all the edges alternate between matched/unmatched.
So you have: unmatched->matched->unmatched->matched->...->unmatched.
Now if you change all the unmatched into matched, and vice versa, you still have a correctly matched graph, only with one more matching.
Repeat, until you can't find such paths.
This is called a method, because you can make different algorithms out of this, with different complexities or for example for weighed graphs. But this is the general idea. ;)

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