We provide the first deterministic data structure that given a weighted undirected graph undergoing edge insertions, processes each update with polylogarithmic amortized update time and answers queries for the distance between any pair of vertices in the current graph with a polylogarithmic approximation in $O(\log \log n)$ time. Prior to this work, no data structure was known for partially dynamic graphs, i.e., graphs undergoing either edge insertions or deletions, with less than $n^{o(1)}$ update time except for dense graphs, even when allowing randomization against oblivious adversaries or considering only single-source distances.
翻译:我们提供了第一个确定性数据结构,根据正插入边缘的加权非方向图形,每个更新过程都使用多元振动振动式更新时间,并回答关于当前图表中任何一对脊椎之间距离的查询,其多元对数近似值为$O(log\log n) 美元。在这项工作之前,对于部分动态图形没有数据结构,即正在边缘插入或删除的图表,除了密度图形之外,更新时间小于$ ⁇ o(1)},即使允许对不明对手随机化或只考虑单一源距离。