# On Light Spanners, Low-treewidth Embeddings and Efficient Traversing in Minor-free Graphs

@article{CohenAddad2020OnLS, title={On Light Spanners, Low-treewidth Embeddings and Efficient Traversing in Minor-free Graphs}, author={Vincent Cohen-Addad and Arnold Filtser and Philip N. Klein and Hung Le}, journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)}, year={2020}, pages={589-600} }

Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A fundamental idea that helps both to understand the structural properties of these metrics and lead to strong algorithmic results is to construct a “small-complexity” graph that approximately preserves distances between pairs of points of the metric. We show the two…

## 16 Citations

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

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

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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.

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