Hungarian algorithm why it works

Watch these videos below to understand how it works. Most of these videos go over the same concept just explained slightly differently. General Maths.

Back to other subjects. How is the Hungarian method applied for obtaining a solution if the matrix is a rectangle? You would first add "dummy" row s or column s to make it square, with the "dummy" value being the highest value from that column or row, respectively. Not Helpful 4 Helpful 8. No, because the values change dramatically, thus changing the equation and the solution. Not Helpful 3 Helpful 2.

Include your email address to get a message when this question is answered. By using this service, some information may be shared with YouTube. If you wish to find a maximum matching rather than a minimum, multiply each number by -1 in step 1, then follow the steps as written. Helpful 11 Not Helpful A key insight here is that adding the same number to all entries in one row or column of the matrix produces a new matrix with the same optimal solution.

This is what allows us to get away with the reduction of the matrix in step 6. Helpful 0 Not Helpful 0. Submit a Tip All tip submissions are carefully reviewed before being published. Related wikiHows How to. How to. Co-authors: 9. Updated: June 4, Hungarian Matching Algorithm Algorithm Brilliant has a very good summary on the Hungarian algorithm for adjacency cost matrix.

Subtract the smallest entry in each row from all the other entries in the row. This will make the smallest entry in the row now equal to 0. Subtract the smallest entry in each column from all the other entries in the column. This will make the smallest entry in the column now equal to 0. Draw lines through the row and columns that have the 0 entries such that the fewest lines possible are drawn.

If there are nn lines drawn, an optimal assignment of zeros is possible and the algorithm is finished. If the number of lines is less than nn, then the optimal number of zeroes is not yet reached. Go to the next step. Find the smallest entry not covered by any line.

Then, go back to Step 3. Example The Brilliant Hungarian algorithm for adjacency cost matrix also comes with a good example. Company Cost for Musician Cost for Chef Cost for Cleaners Company A Company B To avoid duplicating the solution on Brilliant, instead of solving it manually, we will use the existing SciPy linear sum assignment optimizer to solve, and verified using a brute force solver.

The minimum cost from brute force algorithm is: The optimal assignment from Hungarian algorithm is: [ 0, 0 , 1, 1 ]. The minimum cost from Hungarian algorithm is: