Modeling of complex physical systems with Modelica usually leads to the high-index differential algebraic equation system (DAE), index reduction is an important part of solving the high-index DAE. The structure index reduction algorithm is one of the popular methods, but in special cases, it fails. Combinatorial relaxation algorithm can detect and correct the breakdown situation. And the maximum weight matching of bipartite graph is an important part of the combinatorial relaxation algorithm. In order to choose the proper method for the large-scale, dense bipartite graph, this paper provides three implementations of the Hungarian algorithm. The experiment results and the theory show that the BFS single-augmented method is better than others.
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