  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.

Data Structures and Algorithms;Discrete Mathematics;Combinatorics