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

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 n vertices, the amortized operation costs are O (log(2) n) for connectivity, O (log(4) n) for minimum spanning forest, 2-edge connectivity, and O (log(5) n) biconnectivity.