License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.47
URN: urn:nbn:de:0030-drops-124547
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12454/
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Filtser, Arnold

Scattering and Sparse Partitions, and Their Applications

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LIPIcs-ICALP-2020-47.pdf (0.7 MB)

Abstract

A partition ? of a weighted graph G is (σ,τ,Δ)-sparse if every cluster has diameter at most Δ, and every ball of radius Δ/σ intersects at most τ clusters. Similarly, ? is (σ,τ,Δ)-scattering if instead for balls we require that every shortest path of length at most Δ/σ intersects at most τ clusters. Given a graph G that admits a (σ,τ,Δ)-sparse partition for all Δ > 0, Jia et al. [STOC05] constructed a solution for the Universal Steiner Tree problem (and also Universal TSP) with stretch O(τσ²log_τ n). Given a graph G that admits a (σ,τ,Δ)-scattering partition for all Δ > 0, we construct a solution for the Steiner Point Removal problem with stretch O(τ³σ³). We then construct sparse and scattering partitions for various different graph families, receiving many new results for the Universal Steiner Tree and Steiner Point Removal problems.

BibTeX - Entry

@InProceedings{filtser:LIPIcs:2020:12454,
  author =	{Arnold Filtser},
  title =	{{Scattering and Sparse Partitions, and Their Applications}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{47:1--47:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12454},
  URN =		{urn:nbn:de:0030-drops-124547},
  doi =		{10.4230/LIPIcs.ICALP.2020.47},
  annote =	{Keywords: Scattering partitions, sparse partitions, sparse covers, Steiner point removal, Universal Steiner tree, Universal TSP}
}

Keywords: Scattering partitions, sparse partitions, sparse covers, Steiner point removal, Universal Steiner tree, Universal TSP
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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