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

Using ε-bias spaces over F2, we show that the Remote Point Problem (RPP), introduced by Alon et al [APY09], has an NC2 algorithm (achieving the same parameters as [APY09]). We study a generalization of the Remote Point Problem to groups: we replace Fn 2 by Gn for an arbitrary fixed group G. When G is Abelian we give an NC2 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 Gn . All our algorithms for the RPP achieve essentially the same parameters as [APY09].

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Vikraman Arvind, Srikanth Srinivasan
• Keywords: Algorithms, Remote Point Problem, STACS 2010, Theoretical Computer Science, ε-bias Spaces