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2011 26th Annual IEEE Conference on Computational Complexity
Explicit Dimension Reduction and Its Applications
San Jose, California USA
June 08June 11
ISBN: 9780769544113
ASCII Text  x  
Zohar S. Karnin, Yuval Rabani, Amir Shpilka, "Explicit Dimension Reduction and Its Applications," 2012 IEEE 27th Conference on Computational Complexity, pp. 262272, 2011 26th Annual IEEE Conference on Computational Complexity, 2011.  
BibTex  x  
@article{ 10.1109/CCC.2011.20, author = {Zohar S. Karnin and Yuval Rabani and Amir Shpilka}, title = {Explicit Dimension Reduction and Its Applications}, journal ={2012 IEEE 27th Conference on Computational Complexity}, volume = {0}, year = {2011}, issn = {10930159}, pages = {262272}, doi = {http://doi.ieeecomputersociety.org/10.1109/CCC.2011.20}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2012 IEEE 27th Conference on Computational Complexity TI  Explicit Dimension Reduction and Its Applications SN  10930159 SP262 EP272 A1  Zohar S. Karnin, A1  Yuval Rabani, A1  Amir Shpilka, PY  2011 KW  Sample Space KW  Pseudo Random Generator KW  PRG KW  JohnosonLindenstrauss KW  Dimension Reduction KW  Derandomization KW  MaxCut KW  Linear Threshold Function KW  Halfspace KW  Digon VL  0 JA  2012 IEEE 27th Conference on Computational Complexity ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.20
We construct a small set of explicit linear transformationsmapping R^n to R^t, where t=O(log (\gamma^{1}) \eps^{2} ), suchthat the L_2 norm of any vector in R^n is distorted by atmost 1\pm \eps in at least a fraction of 1\gamma of thetransformations in the set. Albeit the tradeoff between thesize of the set and the success probability is suboptimal comparedwith probabilistic arguments, we nevertheless are able to applyour construction to a number of problems. In particular, we use itto construct an \epssample (or pseudorandom generator) forlinear threshold functions on S^{n1}, for \eps = o(1). Wealso use it to construct an \epssample for spherical digons inS^{n1}, for \eps=o(1). This construction leads to anefficient oblivious derandomization of the GoemansWilliamson MAXCUT algorithm and similar approximation algorithms (i.e., weconstruct a small set of hyperplanes, such that for any instancewe can choose one of them to generate a good solution). Our technique for constructing \epssample for linear thresholdfunctions on the sphere is considerably different than previoustechniques that rely on kwise independent sample spaces.
Index Terms:
Sample Space, Pseudo Random Generator, PRG, JohnosonLindenstrauss, Dimension Reduction, Derandomization, MaxCut, Linear Threshold Function, Halfspace, Digon
Citation:
Zohar S. Karnin, Yuval Rabani, Amir Shpilka, "Explicit Dimension Reduction and Its Applications," ccc, pp.262272, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
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