Hungarian algorithm
Bipartite graph formulation

The algorithm can equivalently be described by formulating the problem using a bipartite graph. We have a complete bipartite graph G = (S, T; E) {\displaystyle G=(S,T;E)} with n worker vertices (S) and n job vertices (T), and the edges (E) each have a cost c (i, j) {\displaystyle c(i,j)}. We want to find a perfect matching with a minimum total cost.
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