Scattering and sparse partitions, and their applications

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7 Scopus citations

Abstract

A partition P of a weighted graph G is (σ, τ, ∆)-sparse if every cluster has diameter at most ∆, and every ball of radius ∆/σ intersects at most τ clusters. Similarly, P is (σ, τ, ∆)-scattering if instead for balls we require that every shortest path of length at most ∆/σ intersects at most τ clusters. Given a graph G that admits a (σ, τ, ∆)-sparse partition for all ∆ > 0, Jia et al. [STOC05] constructed a solution for the Universal Steiner Tree problem (and also Universal TSP) with stretch O(τσ2 logτ n). Given a graph G that admits a (σ, τ, ∆)-scattering partition for all ∆ > 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.

Original languageEnglish
Title of host publication47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
EditorsArtur Czumaj, Anuj Dawar, Emanuela Merelli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771382
DOIs
StatePublished - 1 Jun 2020
Externally publishedYes
Event47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany
Duration: 8 Jul 202011 Jul 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume168
ISSN (Print)1868-8969

Conference

Conference47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Country/TerritoryGermany
CityVirtual, Online
Period8/07/2011/07/20

Bibliographical note

Publisher Copyright:
© Arnold Filtser; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).

Keywords

  • Scattering partitions
  • Sparse covers
  • Sparse partitions
  • Steiner point removal
  • Universal Steiner tree
  • Universal TSP

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