Decomposing a Graph into Shortest Paths with Bounded Eccentricity

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.

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