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arXiv · 2302.05951

Fully Dynamic Exact Edge Connectivity in Sublinear Time

Gramoz Goranci·Monika Henzinger·Danupon Nanongkai·Thatchaphol Saranurak·Mikkel Thorup·Christian Wulff-Nilsen
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Abstract

Given a simple $n$-vertex, $m$-edge graph $G$ undergoing edge insertions and deletions, we give two new fully dynamic algorithms for exactly maintaining the edge connectivity of $G$ in $\tilde{O}(n)$ worst-case update time and $\tilde{O}(m^{1-1/31})$ amortized update time, respectively. Prior to our work, all dynamic edge connectivity algorithms either assumed bounded edge connectivity, guaranteed approximate solutions, or were restricted to edge insertions only. Our results provide an affirmative answer to an open question posed by Thorup [Combinatorica'07].

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Gramoz Goranci, Monika Henzinger, Danupon Nanongkai, Thatchaphol Saranurak, Mikkel Thorup, Christian Wulff-Nilsen. 2023-02-12. Fully Dynamic Exact Edge Connectivity in Sublinear Time. https://arxiv.org/abs/2302.05951

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