Kuhn Munkres algorithm Actors
A definition There is a label on every vertex and its value is L[x]. For any edge (x,y) we make sure that L[x] + L[y] ≥ w(x,y).
Another definition We define the equivalent subgraph G'. G' includes all the vertices and all the tight edges. tight: w(x,y) = L[x] + L[y] Actually, we don't care about weight in the G'.
An important lemma If the equivalant subgraph G' has a perfect match, then this match will be the maximum weighted match in G.
New goal Our goal is to find the prefect match in the G'. Welcome Nayun Xu!
A simple description of algorithm procedure Step1. Set a label L[x] for every vertex x. Step2. Get the equivalent subgraph by definition. Step3. If every vertex has been matched , go to Step4. Find a vertex x not matched yet in the left part, and try to find a match vertex y in the right part in the equivalent subgraph. If it is impossible to find a match vertex y for x, then we adjust the vertex label, and go back to Step2, else repeat Step3. Step4. The label now can lead to an equivalent subgraph with a perfect match. And the sum of all the vertex label now is the value of max weight matching.
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Key words in the algorithm 1.vertex label 2.equivalent subgraph 2.find match vertex (network flow or Hungarian algorithm) 3.adjust vertex label
Welcome Kevin Tan
A simple time bound and its proof
A brief introduction to dual problem Actually ...
Thank you for listening!
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