  Given an input graph $G = (V, E)$, an additive emulator $H = (V, E', w)$ is a
sparse weighted graph that preserves all distances in $G$ with small additive
error. A recent line of inquiry has sought to determine the best additive error
achievable in the sparsest setting, when $H$ has a linear number of edges. In
particular, the work of [Kogan and Parter, ICALP 2023], following [Pettie,
ICALP 2007], constructed linear size emulators with $+O(n^{0.222})$ additive
error. It is known that the worst-case additive error must be at least
$+\Omega(n^{2/29})$ due to [Lu, Vassilevska Williams, Wein, and Xu, SODA 2022].
  We present a simple linear-size emulator construction that achieves additive
error $+O(n^{0.191})$. Our approach extends the path-buying framework developed
by [Baswana, Kavitha, Mehlhorn, and Pettie, SODA 2005] and [Vassilevska
Williams and Bodwin, SODA 2016] to the setting of sparse additive emulators.

Data Structures and Algorithms