diff --git a/main.pdf b/main.pdf index 3ebce47..031619c 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.tex b/main.tex index 528bb80..34c145f 100644 --- a/main.tex +++ b/main.tex @@ -201,6 +201,8 @@ Another possible approach for \nonuscut{} would be making the number of demand v Arora, Lee and Naor \cite{arora_euclidean_2005,arora_frechet_2007} proved that there is an embedding from $\ell_2^2$ to $\ell_1$ with distortion $O(\sqrt{\log n}\log \log n)$. This implies an approximation for \nonuscut{} with the same ratio. +Recently the $O(\sqrt{\log n}\log \log n)$ gap has been improved to $\Theta(\sqrt{\log n})$\footnote{STOC '25 \url{https://web.math.princeton.edu/~naor/homepage files/local-growth-STOC.pdf}}. + \section{What problem can I work on?} \subsection{Nealy uniform \scut{}}