Minimum Eccentricity Shortest Path Problem: an Approximation Algorithm and Relation with the k-Laminarity Problem
Computational Complexity
2016-09-16 v1 Discrete Mathematics
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.
Cite
@article{arxiv.1609.04593,
title = {Minimum Eccentricity Shortest Path Problem: an Approximation Algorithm and Relation with the k-Laminarity Problem},
author = {Etienne Birmelé and Fabien De Montgolfier and Léo Planche},
journal= {arXiv preprint arXiv:1609.04593},
year = {2016}
}