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DOI: 10.4230/LIPIcs.ISAAC.2017.15
URN: urn:nbn:de:0030-drops-82621
URL: http://drops.dagstuhl.de/opus/volltexte/2017/8262/
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Birmelé, Etienne ; de Montgolfier, Fabien ; Planche, Léo ; Viennot, Laurent

Decomposing a Graph into Shortest Paths with Bounded Eccentricity

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LIPIcs-ISAAC-2017-15.pdf (0.5 MB)


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.

BibTeX - Entry

@InProceedings{birmel_et_al:LIPIcs:2017:8262,
  author =	{Etienne Birmel{\'e} and Fabien de Montgolfier and L{\'e}o Planche and Laurent Viennot},
  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 =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8262},
  URN =		{urn:nbn:de:0030-drops-82621},
  doi =		{10.4230/LIPIcs.ISAAC.2017.15},
  annote =	{Keywords: Graph Decomposition, Graph Clustering, Distance Labeling, BFS, MESP}
}

Keywords: Graph Decomposition, Graph Clustering, Distance Labeling, BFS, MESP
Seminar: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 04.12.2017


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