eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-07
15:1
15:13
10.4230/LIPIcs.ISAAC.2017.15
article
Decomposing a Graph into Shortest Paths with Bounded Eccentricity
Birmelé, Etienne
de Montgolfier, Fabien
Planche, Léo
Viennot, Laurent
We introduce the problem of hub-laminar decomposition which generalizes that of computing a shortest path with minimum eccentricity (MESP). Intuitively, it consists in decomposing a graph into several paths that collectively have small eccentricity and meet only near their extremities. The problem is related to computing an isometric cycle with minimum eccentricity (MEIC). It is also linked to DNA reconstitution in the context of metagenomics in biology. We show that a graph having such a decomposition with long enough paths can be decomposed in polynomial time with approximated guaranties on the parameters of the decomposition. Moreover, such a decomposition with few paths allows to compute a compact representation of distances with additive distortion. We also show that having an isometric cycle with small eccentricity is related to the possibility of embedding the graph in a cycle with low distortion.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol092-isaac2017/LIPIcs.ISAAC.2017.15/LIPIcs.ISAAC.2017.15.pdf
Graph Decomposition
Graph Clustering
Distance Labeling
BFS
MESP