Sparsification-a technique for speeding up dynamic graph algorithms

@article{Eppstein1992SparsificationaTF,
title={Sparsification-a technique for speeding up dynamic graph algorithms},
author={David Eppstein and Zvi Galil and Giuseppe F. Italiano and Amnon Nissenzweig},
journal={Proceedings., 33rd Annual Symposium on Foundations of Computer Science},
year={1992},
pages={60-69}
}
• Published 24 October 1992
• Computer Science
• Proceedings., 33rd Annual Symposium on Foundations of Computer Science
The authors provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties: minimum spanning forests, best swap, graph connectivity, and graph 2-edge-connectivity, in time O(n/sup 1/2/log(m/n)) per change; 3-edge-connectivity, in time O(n/sup 2/3/) per change; 4-edge-connectivity, in time O(n alpha (n)) per change; k-edge-connectivity, in time O(n log n) per change; bipartiteness, 2-vertex-connectivity, and 3-vertex-connectivity, in…
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