发表机构
Pennsylvania State University（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对动态图可达性等问题，证明了Ω((log n/log log n)²)的时间下界，通过推广Ko的通信游戏框架实现，改进了现有下界并适配多类动态问题。
AI 中文摘要
我们针对支持n节点有向无环图在边插入下可达性查询的动态数据结构，证明了其查询时间与更新时间最大值的Ω((log n/log log n)²)无条件下界。该下界改进了Larsen与Yu[SICOMP 2025]提出的Ω̃(log^(3/2) n)下界，且与目前已知的任何动态问题的最强下界相当。该下界同样适用于增量无向最短路径和子图连通性问题。为证明该结论，我们将Ko[FOCS 2026]提出的框架（该框架针对带内积的Pătraşcu多阶段问题给出了此下界）推广到带不相交性的多阶段问题。我们的主要技术贡献在于证明：Ko的2.5轮多阶段通信游戏中的验证环节，使得单侧腐败界足以替代不相交性所缺乏的差异度。
英文摘要
We prove an $Ω((\log n/\log\log n)^2)$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge insertions. This improves the $\widetildeΩ(\log^{3/2} n)$ lower bound of Larsen and Yu [SICOMP 2025], and matches the strongest lower bound known for any dynamic problem. The same bound holds for incremental undirected shortest paths and subgraph connectivity. To prove it, we bring the recent framework of Ko [FOCS 2026], which gave this bound for Pătraşcu's multiphase problem with Inner Product, to the multiphase problem with Disjointness. Our main technical contribution is to show that verification in Ko's 2.5-round multiphase communication game makes a one-sided corruption bound suffice in place of discrepancy, which Disjointness lacks.
Comments29 pages, 2 figures
