License:
Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2010.2444
URN: urn:nbn:de:0030-drops-24449
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2444/
Arvind, Vikraman ;
Srinivasan, Srikanth
The Remote Point Problem, Small Bias Spaces, and Expanding Generator Sets
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 = {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 |
Collection: |
|
27th International Symposium on Theoretical Aspects of Computer Science |
Issue Date: |
|
2010 |
Date of publication: |
|
09.03.2010 |