# 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…

## 5 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.

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

- Computer Science, MathematicsPODC
- 2022

Euclidean spanners can be viewed as means of compressing the pairwise distances of a d-dimensional Euclidean space into O(n) = O∈,d (n) spanner edges, so that the spanner distances preserve the original distances to within a factor of 1 + ε.

### Light Spanners for High Dimensional Norms via Stochastic Decompositions

- Mathematics, Computer ScienceAlgorithmica
- 2022

This paper shows that any n-point subset of ℓp\documentclass[12pt]{minimal} \usepackage{amsmath} Ã‚¬wasysym} Â£1,000,000 Ã¡¬2,500,000 is a spanner which is both sparse and also light, i.e., its total weight is not much larger than that of the minimum spanning tree.

### Locality-sensitive orderings and applications to reliable spanners

- Computer Science, MathematicsSTOC
- 2022

The theory of LSO’s in non-Euclidean metrics by introducing new types of LOs suitable for general and topologically structured metrics and building reliable spanners for trees and planar graphs with the optimal stretch of 2.

### Low Treewidth Embeddings of Planar and Minor-Free Metrics

- Computer Science, Mathematics
- 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 ((log log n ) 2 ) and additive distortion + (cid:15)D that can be constructed in nearly linear time is obtained.

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