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].

翻译：给定一个进行边插入和删除操作的简单 $n$ 顶点、$m$ 边图 $G$，我们提出了两种新的完全动态算法，分别以 $\tilde{O}(n)$ 最坏情况更新时间和 $\tilde{O}(m^{1-1/31})$ 摊销更新时间，精确维护 $G$ 的边连通性。在我们之前，所有动态边连通性算法要么假设有界边连通性，要么保证近似解，或仅局限于边插入操作。我们的结果对 Thorup [Combinatorica'07] 提出的开放问题给出了肯定回答。