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URN: urn:nbn:de:0030-drops-24449
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The Remote Point Problem, Small Bias Spaces, and Expanding Generator Sets

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Abstract

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 for RPP. We also show the connection to construction of expanding generator sets for the group $\mcG^n$. All our algorithms for the RPP achieve essentially the same parameters as \cite{APY09}.

BibTeX - Entry

@InProceedings{arvind_et_al:LIPIcs:2010:2444,
  author =	{Vikraman Arvind and Srikanth Srinivasan},
  title =	{{The Remote Point Problem, Small Bias Spaces, and Expanding Generator Sets}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{59--70},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2444},
  URN =		{urn:nbn:de:0030-drops-24449},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2444},
  annote =	{Keywords: Small Bias Spaces, Expander Graphs, Cayley Graphs, Remote Point Problem}
}

Keywords: Small Bias Spaces, Expander Graphs, Cayley Graphs, Remote Point Problem
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2010
Date of publication: 2010


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