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 Ω(n^1/6), and that any O(m)-size shortcut set cannot bring it below Ω(n^{1/11}). These improve Hesse's lower bound of Ω(n^{1/17}). By combining these constructions with Abboud and Bodwin's edge-splitting technique, we get additive stretch lower bounds of +Ω(n^{1/13}) for O(n)-size spanners and +Ω(n1/18) for O(n)-size emulators. These improve Abboud and Bodwin's +Ω(n^{1/22}) lower bounds.

Joint work with Seth Pettie.
Shang-En is a PhD student advised by Professor Seth Pettie in Theory Group in the division of Computer Science and Engineering, University of Michigan.
His interested area include Dynamic Graph Data Structures and Graph Algorithms.
Before joining University of Michigan, Shang-En received his Bachelor's degree in mathematics and computer science from National Taiwan University.