问题
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?
回答1:
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.
回答2:
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.
回答3:
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).
回答4:
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.
https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.linear_sum_assignment.html
回答5:
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).
回答6:
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/1398822/the-assignment-problem-a-numpy-function