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Decomposing a Graph into Shortest Paths with Bounded Eccentricity

Authors: Etienne Birmelé, Fabien de Montgolfier, Léo Planche, and Laurent Viennot

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)


Abstract
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.

Cite as

Etienne Birmelé, Fabien de Montgolfier, Léo Planche, and Laurent Viennot. Decomposing a Graph into Shortest Paths with Bounded Eccentricity. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{birmele_et_al:LIPIcs.ISAAC.2017.15,
  author =	{Birmel\'{e}, Etienne and de Montgolfier, Fabien and Planche, L\'{e}o and Viennot, Laurent},
  title =	{{Decomposing a Graph into Shortest Paths with Bounded Eccentricity}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.15},
  URN =		{urn:nbn:de:0030-drops-82621},
  doi =		{10.4230/LIPIcs.ISAAC.2017.15},
  annote =	{Keywords: Graph Decomposition, Graph Clustering, Distance Labeling, BFS, MESP}
}
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