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

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].
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Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.59-70, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science
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Vikraman Arvind, Srikanth Srinivasan. The Remote Point Problem, Small Bias Space, and Expanding Generator Sets. Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.59-70, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science. <inria-00455338>

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