Decomposing a Graph into Shortest Paths with Bounded Eccentricity

Etienne E. Birmelé (1) , Fabien de Montgolfier (2, 3) , Léo Planche (2, 1) , Laurent Viennot (3, 4, 2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
3 GANG - Networks, Graphs and Algorithms
4 LINCS - Laboratory of Information, Network and Communication Sciences

We introduce the problem of hub-laminar decomposition which generalizes that of computing a shortest path with minimum eccentricity. It consists in decomposing a graph into several paths that collectively have small eccentricity and meet only near their extremities. The problem is also related to that of binning appearing in biology in the context of metagenomics. We show that a graph having such a decomposition with sufficient long paths can be decomposed with approximated guar-anties on the parameters of the decomposition.

Mots clés: Graph Decomposition; MESP; Graph Clustering; BFS; Distance Labeling

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

Etienne E. Birmelé, Fabien de Montgolfier, Léo Planche, Laurent Viennot. Decomposing a Graph into Shortest Paths with Bounded Eccentricity. 2017. ⟨hal-01511357v2⟩