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={Dima Grigoriev and Marek 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… CONTINUE READING

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