二端串并联网络中的最远点优化算法
Efficient Farthest-Point Queries in Two-Terminal Series-Parallel Networks
摘要：
考虑沿着网络边缘的点的连续体，即，一个连接的，无向的图，具有正的边权重。我们用加权最短路径距离来度量这些点之间的距离，称为网络距离。在这个度量空间中，我们研究最远点和最远距离。介绍了一种支持两端串并联网络上最远距离和最远点查询的数据结构。此数据结构支持在$O(n \log p)$构造时间之后的$O(k + \log n)$时间中的最远点查询，其中$k$是最远点的数量，$n$是网络的大小，并且需要$p$并行操作来生成网络。
英文摘要：
Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce a data structure supporting queries for the farthest distance and the farthest points on two-terminal series-parallel networks. This data structure supports farthest-point queries in $O(k + \log n)$ time after $O(n \log p)$ construction time, where $k$ is the number of farthest points, $n$ is the size of the network, and $p$ parallel operations are required to generate the network.
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。
