An Alternate Proof of Near-Optimal Light Spanners
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917892329570304 |
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| author | Bodwin, Greg |
| author_facet | Bodwin, Greg |
| contents | In 2016, a breakthrough result of Chechik and Wulff-Nilsen [SODA '16] established that every $n$-node graph $G$ has a $(1+\varepsilon)(2k-1)$-spanner of lightness $O_{\varepsilon}(n^{1/k})$, and recent followup work by Le and Solomon [STOC '23] generalized the proof strategy and improved the dependence on $\varepsilon$. We give a new proof of this result, with the improved $\varepsilon$-dependence. Our proof is a direct analysis of the often-studied greedy spanner, and can be viewed as an extension of the folklore Moore bounds used to analyze spanner sparsity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18647 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Alternate Proof of Near-Optimal Light Spanners Bodwin, Greg Data Structures and Algorithms Discrete Mathematics Combinatorics In 2016, a breakthrough result of Chechik and Wulff-Nilsen [SODA '16] established that every $n$-node graph $G$ has a $(1+\varepsilon)(2k-1)$-spanner of lightness $O_{\varepsilon}(n^{1/k})$, and recent followup work by Le and Solomon [STOC '23] generalized the proof strategy and improved the dependence on $\varepsilon$. We give a new proof of this result, with the improved $\varepsilon$-dependence. Our proof is a direct analysis of the often-studied greedy spanner, and can be viewed as an extension of the folklore Moore bounds used to analyze spanner sparsity. |
| title | An Alternate Proof of Near-Optimal Light Spanners |
| topic | Data Structures and Algorithms Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2305.18647 |