发表机构
ETH Zurich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出全动态图算法，以多对数最坏情况更新时间维护连通性、最小生成树和2-边连通性，改进先前次多项式界限，并指出确定性扩展器分解可带来确定性算法。
AI 中文摘要
我们给出了用于维护图的连通性、最小生成树和2-边连通性的全动态算法，其最坏情况更新时间为多对数级别。我们的算法是随机化的，并且能够以高概率对抗自适应对手。对于最小生成树和2-边连通性问题，这分别改进了Nanongkai、Saranurak和Wulff-Nilsen [FOCS'17]、Jin和Sun [FOCS'21]以及Jin、Sun和Thorup [SODA'24]获得的次多项式更新时间界限。我们算法中唯一的随机化组件是静态扩展器分解的计算，而针对该问题的确定性算法将直接为所有这三个问题提供确定性算法。即使对于连通性问题，这种归约也是新颖的。
英文摘要
We give fully dynamic algorithms for maintaining connectivity, minimum spanning tree, and $2$-edge connectivity of a graph with worst-case polylogarithmic update time. Our algorithms are randomized and succeed with high probability against an adaptive adversary. For the minimum spanning tree and $2$-edge connectivity problems, this improves over the subpolynomial update time bounds obtained by Nanongkai, Saranurak, and Wulff-Nilsen [FOCS'17], Jin and Sun [FOCS'21], and Jin, Sun, and Thorup [SODA'24], respectively. The only randomized component of our algorithms is the computation of static expander decompositions, and a deterministic algorithm for said problem would directly imply deterministic algorithms for all three problems. This reduction is novel even for the connectivity problem.
CommentsTo appear in FOCS 2026
