# Near-Optimal Light Spanners

@article{Chechik2016NearOptimalLS, title={Near-Optimal Light Spanners}, author={Shiri Chechik and Christian Wulff-Nilsen}, journal={ACM Transactions on Algorithms (TALG)}, year={2016}, volume={14}, pages={1 - 15} }

A spanner H of a weighted undirected graph G is a “sparse” subgraph that approximately preserves distances between every pair of vertices in G. We refer to H as a δ-spanner of G for some parameter δ ≥ 1 if the distance in H between every vertex pair is at most a factor δ bigger than in G. In this case, we say that H has stretch δ. Two main measures of the sparseness of a spanner are the size (number of edges) and the total weight (the sum of weights of the edges in the spanner). It is well…

## 31 Citations

Distributed Construction of Light Networks

- Computer Science, MathematicsPODC
- 2020

Efficient distributed algorithms in the CONGEST model for constructing light spanners and SLTs, with near optimal parameters are devised, and a distributed algorithm for constructing nets for arbitrary weighted graphs is developed, generalizing previous algorithms that worked only for unweighted graphs.

Near-Optimal Spanners for General Graphs in (Nearly) Linear Time

- Computer Science, MathematicsSODA
- 2022

The following results on fast constructions of spanners with near-optimal sparsity and lightness are presented, which culminate a long line of work in this area.

NP-hardness and fixed-parameter tractability of the minimum spanner problem

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2018

Weighted Sparse and Lightweight Spanners with Local Additive Error

- MathematicsArXiv
- 2021

This paper gives the first known additive spanners with nontrivial lightness guarantees, and provides a +εW (·, ·) spanner with Oε(n) lightness, and a +(4 + ε)W ( ·,·) spanners with O ε(n ) lightness.

Online Spanners in Metric Spaces

- Mathematics
- 2022

Given a metric space M = (X,δ), a weighted graph G over X is a metric t-spanner of M if for every u, v ∈ X, δ(u, v) ≤ dG(u, v) ≤ t ⋅ δ(u, v), where dG is the shortest path metric in G. In this paper,…

On Notions of Distortion and an Almost Minimum Spanning Tree with Constant Average Distortion

- Computer ScienceSODA
- 2016

This paper shows that any weighted undirected graph admits a spanning tree whose weight is at most (1 + ρ) times that of the MST, providing constant average distortion O(1/ρ2), and obtains an embedding for arbitrary metrics into Euclidean space with optimal prioritized distortion.

Truly Optimal Euclidean Spanners

- Computer Science, Mathematics2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

It is shown that any (1+ε) -spanner must have lightness Ω(ε^-d), and the upper bound on the lightness of the greedy spanner is improved, implying that the greedy (and other) spanners achieve the optimal size.

Towards a Unified Theory of Light Spanners I: Fast (Yet Optimal) Constructions

- Computer Science, MathematicsArXiv
- 2021

This work aims at initiating a unified theory of light spanners by presenting a single framework that can be used to construct lightSpanners in a variety of graph classes by laying the foundations of the theory and applying it to design fast constructions with optimal lightness for several graph classes.

The Greedy Spanner is Existentially Optimal

- Computer Science, MathematicsPODC
- 2016

It is concluded that the greedy spanner achieves near-optimal weight guarantees for both general graphs and doubling metrics, thus resolving two longstanding conjectures in the area.

The Greedy Spanner is Existentially Optimal [ Extended

- Computer Science, Mathematics
- 2016

It is concluded that the greedy spanner achieves near-optimal weight guarantees for both general graphs and doubling metrics, thus resolving two longstanding conjectures in the area.

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