Since an assignment problem can be posed in the form of a single matrix, I am wondering if NumPy has a function to solve such a matrix. So far I have found none. Maybe one of you guys know if NumPy/SciPy has an assignment-problem-solve function?
Edit: In the meanwhile I have found a Python (not NumPy/SciPy) implementation at http://software.clapper.org/munkres/. Still I suppose a NumPy/SciPy implementation could be much faster, right?
No, NumPy contains no such function. Combinatorial optimization is outside of NumPy's scope. It may be possible to do it with one of the optimizers in scipy.optimize but I have a feeling that the constraints may not be of the right form.
NetworkX probably also includes algorithms for assignment problems.
There is now a numpy implementation of the munkres algorithm in scikit-learn under sklearn/utils/linear_assignment_.py its only dependency is numpy. I tried it with some approximately 20x20 matrices, and it seems to be about 4 times as fast as the one linked to in the question. cProfiler shows 2.517 seconds vs 9.821 seconds for 100 iterations.
I was hoping that the newer scipy.optimize.linear_sum_assignment would be fastest, but (perhaps not surprisingly) the Cython library (which does not have pip support) is significantly faster, at least for my use case:
$ python -m timeit -s 'from scipy.optimize import linear_sum_assignment; import numpy as np; np.random.seed(0); c = np.random.rand(20,30)' 'a,b = linear_sum_assignment(c)'
100 loops, best of 3: 3.43 msec per loop
$ python -m timeit -s 'from munkres import munkres; import numpy as np; np.random.seed(0); c = np.random.rand(20,30)' 'a = munkres(c)'
10000 loops, best of 3: 139 usec per loop
$ python -m timeit -s 'from scipy.optimize import linear_sum_assignment; import numpy as np; np.random.seed(0);' 'c = np.random.rand(20,30); a,b = linear_sum_assignment(c)'
100 loops, best of 3: 3.01 msec per loop
$ python -m timeit -s 'from munkres import munkres; import numpy as np; np.random.seed(0)' 'c = np.random.rand(20,30); a = munkres(c)'
10000 loops, best of 3: 127 usec per loop
I saw similar results for sizes between 2x2 and 100x120 (10-40x faster).
Yet another fast implementation, as already hinted by @Matthew: scipy.optimize has a function called linear_sum_assignment. From the docs:
The method used is the Hungarian algorithm, also known as the Munkres or Kuhn-Munkres algorithm.
There is an implementation of the Munkres' algorithm as a python extension module which has numpy support. I've used it successfully on my old laptop. However, it does not work on my new machine - I assume there is a problem with "new" numpy versions (or 64bit arch).
As of version 2.4 (currently in beta), NetworkX solves the problem through nx.algorithms.bipartite.minimum_weight_full_matching. At the time of writing, the implementation uses SciPy's scipy.optimize.linear_sum_assignment under the hood, so expect the same performance characteristics.
来源：https://stackoverflow.com/questions/43162526/performance-of-the-linear-sum-assignment-algorithm