Minimum Eccentricity Shortest Path Problem: an Approximation Algorithm and Relation with the k-Laminarity Problem

TL;DR

This paper improves an approximation algorithm for the Minimum Eccentricity Shortest Path problem from an 8-approximation to a 3-approximation in linear time and explores its relation to the concept of laminarity in graphs.

Contribution

It introduces a more accurate linear-time approximation algorithm for MESP and establishes tight bounds linking MESP to laminarity parameters.

Findings

Developed a linear-time 3-approximation algorithm for MESP.

Analyzed the double-BFS procedure to enhance approximation quality.

Established tight bounds between MESP and laminarity parameters.

Abstract

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{\"o}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.