Boolean matching algorithm based on the perfect matching of the bipartite graph

This paper presents an improved Boolean matching algorithm based on the perfect matching of the bipartite graph. By transforming the mapping between Boolean variables into the problem of the perfect matching of the bipartite graph, this improved algorithm can overcome the shortcoming of the original algorithm, i.e., lengthy computation time caused by the excessive mapping terms. It is shown through the experimental results on MCNC benchmarks that the improved algorithm can reduce the computation time by about 21% compared to the original algorithm. Also, the concept of the strongly mapping between Boolean variables is presented, which is the generalization of the conventional Boolean variable mapping.