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arXiv · 2305.18647

An Alternate Proof of Near-Optimal Light Spanners

Greg Bodwin
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Abstract

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.

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Greg Bodwin. 2023-05-29. An Alternate Proof of Near-Optimal Light Spanners. https://doi.org/10.46298/theoretics.25.2

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