Lower Bounds on Sparse Spanners, Emulators, and Diameter-reducing shortcuts
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.
additive spanners
emulators
shortcutting directed graphs
Theory of computation~Sparsification and spanners
26:1-26:12
Regular Paper
Shang-En
Huang
Shang-En Huang
University of Michigan, USA
Seth
Pettie
Seth Pettie
University of Michigan, USA
10.4230/LIPIcs.SWAT.2018.26
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Shang-En Huang and Seth Pettie
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