在亚线性时间内的完全动态精确边连通性

Proceedings of the ... Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2023-02-12 DOI:10.1137/1.9781611977554.ch3

Gramoz Goranci, M. Henzinger, Danupon Nanongkai, Thatchaphol Saranurak, M. Thorup, Christian Wulff-Nilsen

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引用次数: 1

摘要

给定一个简单的$n$顶点，$m$边的图$G$，在$\tilde{O}(n)$最坏情况更新时间和$\tilde{O}(m^{1-1/16})$平摊更新时间内，我们分别给出了两种新的完全动态算法来精确地保持$G$的边连通性。在我们的工作之前，所有动态边缘连接算法都假设有界边缘连接，保证近似解，或者仅限于边缘插入。我们的结果肯定地回答了Thorup [Combinatorica'07]提出的一个开放性问题。

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Fully Dynamic Exact Edge Connectivity in Sublinear Time

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 $\tilde{O}(m^{1-1/16})$ amortized update time, respectively. Prior to our work, all dynamic edge connectivity algorithms assumed bounded edge connectivity, guaranteed approximate solutions, or were restricted to edge insertions only. Our results answer in the affirmative an open question posed by Thorup [Combinatorica'07].

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