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41st Annual Symposium on Foundations of Computer Science
Stable distributions, pseudorandom generators, embeddings and data stream computation
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
P. Indyk, "Stable distributions, pseudorandom generators, embeddings and data stream computation," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 189, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892082, author = {P. Indyk}, title = {Stable distributions, pseudorandom generators, embeddings and data stream computation}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {189}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892082}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Stable distributions, pseudorandom generators, embeddings and data stream computation SN  02725428 SP EP A1  P. Indyk, PY  2000 KW  probability; random number generation; stable distributions; pseudorandom generators; embeddings; data stream computation; bounded space; dimensionality reduction VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: we show how to maintain (using only O(log n//spl epsiv//sup 2/) words of storage) a sketch C(p) of a point p/spl isin/l/sub 1//sup n/ under dynamic updates of its coordinates, such that given sketches C(p) and C(q) one can estimate pq/sub 1/ up to a factor of (1+/spl epsiv/) with large probability. We obtain another sketch function C' which maps l/sub 1//sup n/ into a normed space l/sub 1//sup m/ (as opposed to C), such that m=m(n) is much smaller than n; to our knowledge this is the first dimensionality reduction lemma for l/sub 1/ norm we give an explicit embedding of l/sub 2//sup n/ into l/sub l//sup nO(log n)/ with distortion (1+1/n/sup /spl theta/(1)/) and a nonconstructive embedding of l/sub 2//sup n/ into l/sub 1//sup O(n)/ with distortion (1+/spl epsiv/) such that the embedding can be represented using only O(n log/sup 2/ n) bits (as opposed to at least n/sup 2/ used by earlier methods).
Index Terms:
probability; random number generation; stable distributions; pseudorandom generators; embeddings; data stream computation; bounded space; dimensionality reduction
Citation:
P. Indyk, "Stable distributions, pseudorandom generators, embeddings and data stream computation," focs, pp.189, 41st Annual Symposium on Foundations of Computer Science, 2000
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