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

Vikraman Arvind; Srikanth Srinivasan

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arXiv · 0909.5313

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

Vikraman Arvind·Srikanth Srinivasan

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Abstract

Using $ε$-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 $ε$-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].

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Vikraman Arvind, Srikanth Srinivasan. 2010-02-03. The Remote Point Problem, Small Bias Space, and Expanding Generator Sets. https://arxiv.org/abs/0909.5313

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