# The Remote Point Problem, Small Bias Space, and Expanding Generator Sets

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1 IMSc - Institute of Mathematical Sciences India

Abstract : Using $\epsilon$-bias spaces over $F 2$, we show that the Remote Point Problem RPP, introduced by Alon et al APY09, has an $NC^2$ algorithm achieving the same parameters as APY09. We study a generalization of the Remote Point Problem to groups: we replace $F^n$ by $G^n$ for an arbitrary fixed group $G$. When $G$ is Abelian, we give an $NC^2$ algorithm for RPP, again using $\epsilon$-bias spaces. For nonabelian $G$, we give a deterministic polynomial-time algorithm for RPP. We also show the connection to construction of expanding generator sets for the group $G^n$. All our algorithms for the RPP achieve essentially the same parameters as APY09.

Keywords : small bias spaces expander graphs cayley graphs remote point problem

Autor: Vikraman Arvind - Srikanth Srinivasan -

Fuente: https://hal.archives-ouvertes.fr/

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