# The matching problem for bipartite graphs with polynomially bounded permanents is in NC

@article{Grigoriev1987TheMP, title={The matching problem for bipartite graphs with polynomially bounded permanents is in NC}, author={D. Grigoriev and M. Karpinski}, journal={28th Annual Symposium on Foundations of Computer Science (sfcs 1987)}, year={1987}, pages={166-172} }

It is shown that the problem of deciding and constructing a perfect matching in bipartite graphs G with the polynomial permanents of their n × n adjacency matrices A (perm(A) = nO(1)) are in the deterministic classes NC2 and NC3, respectively. We further design an NC3 algorithm for the problem of constructing all perfect matchings (enumeration problem) in a graph G with a permanent bounded by O(nk). The basic step was the development of a new symmetric functions method for the decision… Expand

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