Sparsification—a technique for speeding up dynamic graph algorithms

@article{Eppstein1997SparsificationaTF,
  title={Sparsification—a technique for speeding up dynamic graph algorithms},
  author={David Eppstein and Zvi Galil and Giuseppe F. Italiano and Amnon Nissenzweig},
  journal={J. ACM},
  year={1997},
  volume={44},
  pages={669-696}
}
We provide data strutures that maintain a graph as edges are inserted and deleted, and keep track of the following properties with the following times: minimum spanning forests, graph connectivity, graph 2-edge connectivity, and bipartiteness in time<italic>O</italic>(<italic>n</italic><supscrpt>1/2</supscrpt>) per change; 3-edge connectivity, in time <italic>O</italic>(<italic>n</italic><supscrpt>2/3</supscrpt>) per change; 4-edge connectivity, in time <italic>O</italic>(<italic>n</italic… 
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