• Corpus ID: 244709353

# 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}
}
• Published 25 November 2021
• Computer Science, Mathematics
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…
1 Citations

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## References

SHOWING 1-10 OF 33 REFERENCES

### Near-Optimal Decremental SSSP in Dense Weighted Digraphs

• Computer Science
2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
• 2020
The framework effectively allows us to reduce SSSP in general graphs to the same problem in directed acyclic graphs (DAGs) and overcomes its limitations by introducing a significantly more powerful abstraction, as well as a different core subroutine.

### Lower Bounds on Sparse Spanners, Emulators, and Diameter-reducing shortcuts

• Computer Science
SWAT
• 2018
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

### All-Pairs LCA in DAGs: Breaking through the O(n2.5) barrier

• Mathematics, Computer Science
SODA
• 2021
An algorithm for finding an LCA for all pairs of vertices in a DAG, which represents the first improvement on the running times for this problem in the last 13 years.

### Decremental SSSP in Weighted Digraphs: Faster and Against an Adaptive Adversary

• Computer Science, Mathematics
SODA
• 2020