Fast Spectral Signing for Vector Balancing
A deterministic algorithm that finds signs with $\|A\varepsilon\|_\infty<99$ using $O(mn+n^{\omega+2}\log^3 n)$ arithmetic operations, where $\omega>2$ is any fixed attainable matrix-multiplication exponent; with the current bounds on $\omega$ this is $\widetilde O(mn+n^{4.372})$.