The Remote Point Problem, Small Bias Spaces, and Expanding Generator Sets

Vikraman Arvind & Srikanth Srinivasan
Using $\varepsilon$-bias spaces over $\F_2$, we show that the Remote Point Problem (RPP), introduced by Alon et al \cite{APY09}, has an $\NC^2$ algorithm (achieving the same parameters as \cite{APY09}). We study a generalization of the Remote Point Problem to groups: we replace $\F_2^n$ by $\mcG^n$ for an arbitrary fixed group $\mcG$. When $\mcG$ is Abelian we give an $\NC^2$ algorithm for RPP, again using $\varepsilon$-bias spaces. For nonabelian $\mcG$, we give a deterministic polynomial-time algorithm...