# Near-optimal fully-dynamic graph connectivity

@inproceedings{Thorup2000NearoptimalFG, title={Near-optimal fully-dynamic graph connectivity}, author={Mikkel Thorup}, booktitle={STOC '00}, year={2000} }

In this paper we present near-optimal bounds for fullydynamic graph connectivity which is the most basic nontrivial fully-dynamic graph problem. Connectivity queries are supported in O(log n/log log log n) time while the updates are supported in O(log n(log log n) 3) expected amortized time. The previous best update time was O((log n)2). Our new bound is only doubly-logarithmic factors from a general cell probe lower bound of f2(log n~ log log n). Our algorithm runs on a pointer machine, and…

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## 189 Citations

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