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

Authors:
Jacob Holm;Kristian de Lichtenberg;Mikkel Thorup
Affiliations:
University of Copenhagen, Copenhagen, Denmark;University of Copenhagen, Copenhagen, Denmark;AT&T Labs---Research, Florham Park, New Jersey
Venue:
Journal of the ACM (JACM)
Year:
2001

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Abstract

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(log2 n) for connectivity, O(log4 n) for minimum spanning forest, 2-edge connectivity, and O(log5 n) biconnectivity.