Creative Commons Attribution 4.0 license (CC BY 4.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2021.33
URN: urn:nbn:de:0030-drops-138328
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13832/
Eppstein, David ; Khodabandeh, Hadi
On the Edge Crossings of the Greedy Spanner
| pdf-format: |
|
Abstract
The greedy t-spanner of a set of points in the plane is an undirected graph constructed by considering pairs of points in order by distance, and connecting a pair by an edge when there does not already exist a path connecting that pair with length at most t times the Euclidean distance. We prove that, for any t > 1, these graphs have at most a linear number of crossings, and more strongly that the intersection graph of edges in a greedy t-spanner has bounded degeneracy. As a consequence, we prove a separator theorem for greedy spanners: any k-vertex subgraph of a greedy spanner can be partitioned into sub-subgraphs of size a constant fraction smaller, by the removal of O(√k) vertices. A recursive separator hierarchy for these graphs can be constructed from their planarizations in linear time, or in near-linear time if the planarization is unknown.
BibTeX - Entry
@InProceedings{eppstein_et_al:LIPIcs.SoCG.2021.33,
author = {Eppstein, David and Khodabandeh, Hadi},
title = {{On the Edge Crossings of the Greedy Spanner}},
booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)},
pages = {33:1--33:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-184-9},
ISSN = {1868-8969},
year = {2021},
volume = {189},
editor = {Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13832},
URN = {urn:nbn:de:0030-drops-138328},
doi = {10.4230/LIPIcs.SoCG.2021.33},
annote = {Keywords: Geometric Spanners, Greedy Spanners, Separators, Crossing Graph, Sparsity}
}
| Keywords: | Geometric Spanners, Greedy Spanners, Separators, Crossing Graph, Sparsity | |
| Seminar: | 37th International Symposium on Computational Geometry (SoCG 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 02.06.2021 |
