# New Diameter-Reducing Shortcuts and Directed Hopsets: Breaking the $\sqrt{n}$ Barrier

@inproceedings{Kogan2021NewDS, title={New Diameter-Reducing Shortcuts and Directed Hopsets: Breaking the \$\sqrt\{n\}\$ Barrier}, author={Shimon Kogan and Merav Parter}, year={2021} }

For an n-vertex digraph G = (V, E), a 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 ∪ 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…

## One Citation

### Closing the Gap Between Directed Hopsets and Shortcut Sets

- MathematicsArXiv
- 2022

For an n-vertex directed graph G = ( V, E ) , a β - shortcut set H is a set of additional edges H ⊆ V × V such that G ∪ H has the same transitive closure as G , and for every pair u, v ∈ V , there is…

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