Matchpair function to solve linear assignment problem

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Danish Nasir 2021-8-16

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https://ww2.mathworks.cn/matlabcentral/answers/898997-matchpair-function-to-solve-linear-assignment-problem

评论： Danish Nasir 2021-8-16

1. I want to know whether Hungarian algorithm is an exact solution algorithm or a heuristic?

2. MATLAB has inbuilt fucntion Matchpair to solve linear assignment problem. What is the difference between Hungarian and Matchpair ( in terms of Time complexity, approach,exact or heuristic)?

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Steven Lord 2021-8-16

For more information about the algorithm matchpairs implements, see the reference listed in the References section on the documentation page for the matchpairs function.

Danish Nasir 2021-8-16

I already read the documentation. But time complexity of Matchpair is not mentioned in the documentation. Matchpair is fast but quality of optimal solution is quite inferior compared to Hungarian.

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Answer 1

Walter Roberson 2021-8-16

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The Hungarian Algorithm is an exact solution for linear assignment problems.

https://en.wikipedia.org/wiki/Hungarian_algorithm

I do not know anything about the algorithm used by matchpair() but I do notice that it handles the possibility of rows without matches (such as idle workers), which the Hungarian Algorithm by itself does not handle.