关于带环的动态双向 Dyck 可达性的一点注记
A Note on Dynamic Bidirected Dyck-Reachability with Cycles
AI总结：
本文指出Li等人[2022]的动态Dyck可达性算法在合并图存在环时边删除过程无法正确更新权重，并讨论了环情况与时间复杂度。
摘要：
最近，Li等人[2022]提出了一种用于双向图的动态Dyck可达性算法。其基本思想是基于更新一种称为合并图 $G_m$ 的数据结构中的边权重。正如 Krishna等人[2023]所指出的，Li等人[2022]算法中描述的边删除过程在 $G_m$ 中存在环时无法正确更新权重。本注记讨论了环的情况和时间复杂度。
英文摘要：
Recently, Li et al. [2022] presented a dynamic Dyck-reachability algorithm for bidirected graphs. The basic idea is based on updating edge weights in a data structure called the merged graph $G_m$. As noted in Krishna et al. [2023], the edge deletion procedure described in the algorithm of Li et al. [2022] cannot properly update the weights in the presence of cycles in $G_m$. This note discusses the cycle case and the time complexity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
