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

Etienne E. Birmelé (1) , Fabien de Montgolfier (2, 3) , Léo Planche (1, 3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 GANG - Networks, Graphs and Algorithms
3 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

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 Völkel 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.

Mots clés: k-Laminar Graph; Approximation Algorithms; BFS; Eccentricity; Diameter; Graph theory; Graph search

Domaines: Algorithme et structure de données [cs.DS]

Etienne E. Birmelé, Fabien de Montgolfier, Léo Planche. Minimum Eccentricity Shortest Path Problem: An Approximation Algorithm and Relation with the k-Laminarity Problem. COCOA 2016, Combinatorial Optimization and Applications - 10th International Conference, Dec 2016, Hong Kong, China. pp.216 - 229, ⟨10.1007/978-3-319-48749-6_16⟩. ⟨hal-01424469⟩