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DOI: 10.4230/LIPIcs.ICALP.2020.47
URN: urn:nbn:de:0030-drops-124547
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12454/
Filtser, Arnold
Scattering and Sparse Partitions, and Their Applications
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Abstract
A partition 𝒫 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, 𝒫 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 | |
| Seminar: | 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 29.06.2020 |
