Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity

@article{Holm2001PolylogarithmicDF,
  title={Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity},
  author={Jacob Holm and Kristian de Lichtenberg and Mikkel Thorup},
  journal={J. ACM},
  year={2001},
  volume={48},
  pages={723-760}
}
Deterministic fully dynamic graph algorithms are presented for connectivity, minimum spanning tree, 2-edge connectivity, and biconnectivity. Assuming that we start with no edges in a graph with <i>n</i> vertices, the amortized operation costs are <i>O</i>(log<sup>2</sup> <i>n</i>) for connectivity, <i>O</i>(log<sup>4</sup> <i>n</i>) for minimum spanning forest, 2-edge connectivity, and <i>O</i>(log<sup>5</sup> <i>n</i>) biconnectivity. 

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