2026-08-18T16:12:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8852 2024-03-06T10:42:48Z ddc:004 open_access

Lower Bounds on Sparse Spanners, Emulators, and Diameter-reducing shortcuts Huang, Shang-En Pettie, Seth additive spanners emulators shortcutting directed graphs We prove better lower bounds on additive spanners and emulators, which are lossy compression schemes for undirected graphs, as well as lower bounds on shortcut sets, which reduce the diameter of directed graphs. We show that any O(n)-size shortcut set cannot bring the diameter below Omega(n^{1/6}), and that any O(m)-size shortcut set cannot bring it below Omega(n^{1/11}). These improve Hesse's [Hesse, 2003] lower bound of Omega(n^{1/17}). By combining these constructions with Abboud and Bodwin's [Abboud and Bodwin, 2017] edge-splitting technique, we get additive stretch lower bounds of +Omega(n^{1/13}) for O(n)-size spanners and +Omega(n^{1/18}) for O(n)-size emulators. These improve Abboud and Bodwin's +Omega(n^{1/22}) lower bounds. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shang-En Huang and Seth Pettie 2018 Is Part Of LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2018.26 urn:nbn:de:0030-drops-88521 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.26 eng https://creativecommons.org/licenses/by/3.0/legalcode