Bisimplicial edges in bipartite graphs

@article{Bomhoff2013BisimplicialEI,
  title={Bisimplicial edges in bipartite graphs},
  author={Matthijs Bomhoff and Bodo Manthey},
  journal={Discrete Applied Mathematics},
  year={2013},
  volume={161},
  pages={1699-1706}
}
Bisimplicial edges in bipartite graphs are closely related to pivots in Gaussian elimination that avoid turning zeroes into non-zeroes. We present a new deterministic algorithm to find such edges in bipartite graphs. The expected time complexity of our new algorithm is O ( n2 log n ) on random bipartite graphs in which each edge is present with a fixed probability p, a polynomial improvement over the fastest algorithm found in the existing literature.