Hop-Constrained Metric Embeddings and their Applications

  title={Hop-Constrained Metric Embeddings and their Applications},
  author={Arnold Filtser},
  journal={2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)},
  • Arnold Filtser
  • Published 28 June 2021
  • Computer Science
  • 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
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

Figures and Tables from this paper

Low Treewidth Embeddings of Planar and Minor-Free Metrics
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
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
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
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


Tree embeddings for hop-constrained network design
It is shown that hop-constrained distances can be approximated by distributions over ``partial tree metrics'' and built into a powerful and versatile algorithmic tool which, similarly to classic probabilistic tree embeddings, reduces hop- Constrained problems in general graphs to hop-unconstraining problems on trees.
Hopsets with Constant Hopbound, and Applications to Approximate Shortest Paths
  • Michael Elkin, Ofer Neiman
  • Computer Science, Mathematics
    2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2016
The first construction of sparse hopsets with a constant number of hops is exhibited, and the applicability of the results for the fundamental problem of computing approximate shortest paths from s sources is demonstrated.
Near-Additive Spanners and Near-Exact Hopsets, A Unified View
An intriguing phenomenon is explored, Thorup-Zwick's later construction of near-additive spanners was shown to provide hopsets with analogous (to that of \cite{TZ06}) properties, and the basic proof techniques used for these results are sketched.
Deterministic Constructions of Approximate Distance Oracles and Spanners
The first deterministic linear time algorithm for constructing optimal spanners of weighted graphs is obtained by derandomizing the O(km) expected time algorithm of Baswana and Sen for constructing (2k–1)-spanners of size O(kn) of weighted undirected graphs without incurring any asymptotic loss in the running time or in the size of the spanners produced.
Ramsey Spanning Trees and their Applications
The natural extension of the metric Ramsey problem to graphs is studied, and the notion of Ramsey Spanning Trees is introduced, which provides the state-of-the-art deterministic construction of a distance oracle.
On Light Spanners, Low-treewidth Embeddings and Efficient Traversing in Minor-free Graphs
The paper designs the first FPT approximation scheme for bounded-capacity vehicle routing on bounded-treewidth graphs (parameterized by the treewidth) and shows the two following structural results for minor-free metrics.
Relaxed Voronoi: A Simple Framework for Terminal-Clustering Problems
The main contribution is to demonstrate that the Relaxed-Voronoi algorithm is applicable to restricted metrics, and actually leads to relatively simple algorithms and analyses.
Prioritized Metric Structures and Embedding
This paper shows that given a priority ranking of the graph vertices one can devise a metric data structure in which the stretch incurred by any pair containing a vertex xj will depend on the rank j of the vertex, and shows that other important parameters, such as the label size and (in some sense) the dimension, may depend only on j.
Labelings vs. Embeddings: On Distributed Representations of Distances
The worst-case bound for label size often ``translates'' to a prioritized one, but also a surprising exception to this rule when comparing the classical and prioritized settings.
On Strong Diameter Padded Decompositions
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.