skip to main content

TCS+ Talk

Wednesday, February 23, 2022
10:00am to 11:00am
Add to Cal
Online Event
New Diameter Reducing Shortcuts: Breaking the $O(\sqrt{n})$ Barrier
Merav Parter, Weizmann Institute of Science,

Abstract: For an $n$-vertex digraph $G=(V,E)$, a \emph{shortcut set} is a (small) subset of edges $H$ taken from the transitive closure of $G$ that, when added to $G$ guarantees that the diameter of $G \cup H$ is small. Shortcut sets, introduced by Thorup in 1993, have a wide range of applications in algorithm design, especially in the context of parallel, distributed and dynamic computation on directed graphs. A folklore result in this context shows that every $n$-vertex digraph admits a shortcut set of linear size (i.e., of $O(n)$ edges) that reduces the diameter to $\widetilde{O}(\sqrt{n})$. Despite extensive research over the years, the question of whether one can reduce the diameter to $o(\sqrt{n})$ with $\widetilde{O}(n)$ shortcut edges has been left open.

In this talk, I will present the first improved diameter-sparsity tradeoff for this problem, breaking the $\sqrt{n}$ diameter barrier. Specifically, we show an $O(n^{\omega})$-time randomized algorithm for computing a linear shortcut set that reduces the diameter of the digraph to $\widetilde{O}(n^{1/3})$. We also extend our algorithms to provide improved $(\beta,\epsilon)$ hopsets for $n$-vertex weighted directed graphs.

Joint work with Shimon Kogan.

  • Watching the live stream. At the announced start time of the talk (or a minute before), a live video stream will be available on our "next talk" page. Simply connect to the page and enjoy the talk. No webcam or registration is needed. Questions and comments during the talk are welcome (text only, unfortunately); simply post a comment below the live video stream on YouTube.
  • Watching the recorded talk offline. The recorded talk will be made available shortly after the talk ends on our YouTube page. (Please leave a comment if you enjoyed it!)
For more information, please contact Bonnie Leung by email at [email protected].