无$K_{2,3}$子式图的最小偏心度最短路径
Minimum eccentricity shortest paths of $K_{2,3}$-minor-free graphs
AI总结：
本文针对无$K_{2,3}$子式图的最小偏心度最短路径（MESP）问题，提出$O(n^4)$时间算法，输入为仙人掌图时算法时间复杂度为三次方级，为该类图的MESP问题提供了可行的高效求解方案。
AI中文摘要：
给定简单、无向、无权图$G$和整数$R$，最小偏心度最短路径（MESP）问题的目标是判断$G$中是否存在等距路径$P$，使得图中每个顶点到$P$中最近顶点的距离不超过$R$。本文证明，MESP在无$K_{2,3}$子式图上存在$O(n^4)$时间的算法；当输入限定为仙人掌图时，该算法的运行时间为三次方级。
英文摘要：
Given a simple, undirected, and unweighted graph $G$, and an integer $R$, the objective of the \textsc{Minimum Eccentricity Shortest Path (MESP)} is to decide whether there exists an \emph{isometric path} $P$ in $G$ such that the distance from every vertex in the graph to its nearest vertex in $P$ is at most $R$. In this paper, we prove that MESP admits an $O(n^4)$-time algorithm on $K_{2,3}$-minor-free graphs. Our algorithm has a cubic running time when the inputs are restricted to a cactus.
