# Hop-Constrained Metric Embeddings and their Applications

@article{Filtser2022HopConstrainedME, title={Hop-Constrained Metric Embeddings and their Applications}, author={Arnold Filtser}, journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)}, year={2022}, pages={492-503} }

In network design problems, such as compact routing, the goal is to route packets between nodes using the (approximated) shortest paths. A desirable property of these routes is a small number of hops, which makes them more reliable, and reduces the transmission costs. Following the overwhelming success of stochastic tree embeddings for algorithmic design, Haeupler, Hershkowitz, and Zuzic (STOC'21) studied hop-constrained Ramsey-type metric embeddings into trees. Specifically, embedding $f: G(V…

## 4 Citations

Low Treewidth Embeddings of Planar and Minor-Free Metrics

- Computer Science, MathematicsArXiv
- 2022

A new embedding technique to improve the treewidth bound of Cohen-Addad et al. is devised and a deterministic embedding of planar graphs of diameter D into graphs oftreewidth O and additive distortion + (cid:15)D that can be constructed in nearly linear time is obtained.

On Strong Diameter Padded Decompositions

- MathematicsAPPROX-RANDOM
- 2019

The state of the art for weak and strong decompositions for free graphs are matched, and aparse cover scheme is constructed to construct $(O(d),\tilde{O}(d))$-sparsecover scheme for such graphs.

Locality-Sensitive Orderings and Applications to Reliable Spanners

- Computer Science, Mathematics
- 2021

This paper develops the theory of LSO’s in non-Euclidean metrics by introducing new types of LOs suitable for general and topologically structured metrics, and uses them to construct reliable spanners with improved stretch and sparsity parameters.

Can't See The Forest for the Trees: Navigating Metric Spaces by Bounded Hop-Diameter Spanners

- MathematicsArXiv
- 2021

Spanners for metric spaces have been extensively studied, both in general metrics and in restricted classes, perhaps most notably in low-dimensional Euclidean spaces — due to their numerous…

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