Munkres Python Package 未生成最大总数

Question

I am currently writing an algorithm to match users by compatibility score. So each user has a compatibility score with each of the other users. The goal is to maximize the total compatibility score. I am using the munkres python package to get the indices and then filtering the duplicates. (ie if user1 matches with user2, we remove the match with user2 and user1).

Here is an example matrix: (DISALLOWED in place where a user cannot be matched with themselves.)

matrix = [[DISALLOWED, 2, 5, 7, 13, 10],
         [2, DISALLOWED, 25, 13, 5, 14],
         [5, 25, DISALLOWED, 21, 100, 17],
         [7, 13, 21, DISALLOWED, 70, 2],
         [13, 5, 100, 70, DISALLOWED, 200],
         [10, 14, 17, 2, 200, DISALLOWED]]

Here is what I have tried. It works for this smaller matrix example I gave but is not giving the optimal score for the larger dataset. I know the total score is not optimal as a non-optimized algorithm (simply sorting the scores and matching each user in order) is generating a much higher score.

def optimize(matrix):
    optimal_matrix = make_cost_matrix(matrix, lambda cost: (sys.maxsize - cost) if
                                    (cost != DISALLOWED) else DISALLOWED)

    m = Munkres()
    indexes = m.compute(optimal_matrix)
    
    matches = []
    for row, column in indexes:
        value = matrix[row][column]
        match = [row, column, value]
        matches.append(match)

    matches.sort(key=thirdValue, reverse=True)

    seen = []
    total = 0
    for match in matches:

        if match[0] not in seen and match[1] not in seen:
            total += match[2]
            seen.append(match[0])
            seen.append(match[1])
    print(total)

Is there a certain matrix that would break my code? Any help or pointers would be appreciated.

Answer 1

The Hungarian Algorithm is for "bipartite" graphs, but you don't have a bipartite graph. A bipartite graph is one in which you have two distinct sets of nodes. For example: assigning workers to jobs. Nodes within a set do not connect to each other; a worker can be assigned to a job, or a job to a worker, but workers are not assigned to workers nor jobs assigned to jobs. In your case you are trying to assign users to other users . That is, you only have one set, not two.

By marking the diagonal DISALLOWED you are preventing a user from being matched with themselves, but you aren't preventing a user from being matched with more than one other user. For example, with only four users who all have the same compatibility:

	A	B	C	D
A		0	0	0
B	0		0	0
C	0	0		0
D	0	0	0

A matched with C
B matched with D
C matched with B
D matched with A

is a valid result for the Hungarian algorithm, but is not valid for your situation. I don't know that this is what's happening, but it could happen, so you need to use a different algorithm.