最小偏心率最短路问题的一种近似算法及其与k-分层问题的关系
Minimum Eccentricity Shortest Path Problem: an Approximation Algorithm and Relation with the k-Laminarity Problem
摘要：
最小偏心率最短路径（MESP）问题是确定图中最小偏心率的最短路径（其长度是其端点之间的距离的路径）。它是由Dragan和Leitert [9]介绍的，他们描述了一种线性时间算法，这是问题的8-近似。本文对该算法中的双BFS过程进行了深入的研究，并对其进行了扩展，得到了一个线性时间的3-近似算法。此外，我们研究了MESP问题与V{<$}lkel等人[12]引入的层状性概念之间的联系，对应于其对直径的限制（即最大长度的最短路径），并显示了MESP和层状性参数之间的紧密界限。
英文摘要：
The Minimum Eccentricity Shortest Path (MESP) Problem consists in determining a shortest path (a path whose length is the distance between its extremities) of minimum eccentricity in a graph. It was introduced by Dragan and Leitert [9] who described a linear-time algorithm which is an 8-approximation of the problem. In this paper, we study deeper the double-BFS procedure used in that algorithm and extend it to obtain a linear-time 3-approximation algorithm. We moreover study the link between the MESP problem and the notion of laminarity, introduced by V{ö}lkel et al [12], corresponding to its restriction to a diameter (i.e. a shortest path of maximum length), and show tight bounds between MESP and laminarity parameters.
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