The Hungarian algorithm finds a maximum independent edge set on a graph. The algorithm starts with any matching M and constructs a tree via a breadth-first search to find an augmenting path, namely a path P that starts and finishes at unmatched vertices whose first and last edges are not in M and whose edges alternate being outside and inside M. If the search succeeds, the symmetric difference of M and the edges in P yields a matching with one more edge than M. That edge is added, and then another search is performed for a new augmenting path. If the search is unsuccessful, the algorithm terminates and M must be the largest-size matching.

As an added bonus, the tree data provides a vertex cover.

If the tree search is unsuccessful, as it is at the end, then the size of the vertex cover is the same as the size of the matching, which proves that the final matching has the maximum size possible.

For More information Click Here : 

https://essayassignmenthelp.com.au/hungarian-algorithm-calculator.html