# Hungarian method: seemingly different algorithms from different sources?

When I look online for examples of the Hungarian method for solving the min-weight assignment problem, for example here, it involves iterating on the cost matrix; subtracting entries from the rows and columns.

However, in section 17.2 of the book, Combinatorial optimization polyhedra and efficiency by Schrijver, a seemingly different algorithm is presented. Here, we start with a matching $$M$$, assign $$W_M$$ and $$U_M$$ as the edges on the left and right of the bi-partite graph that haven't been covered by the matching, describe path lengths as $$l_e=w_e$$ if the edge is in $$M$$ and $$l_e=-w_e$$ otherwise and find a min path from $$U_M$$ to $$W_M$$. Then, reset $$M$$ to $$M'$$, the symmetric difference between the path $$P$$ and $$M$$.

These two algorithms seem very different to me. Are they somehow the same under the cover?