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Stable distributions, pseudorandom generators, embeddings and data stream computation

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1 Author(s)
Indyk, P. ; Stanford Univ., CA, USA

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/ε2) words of storage) a sketch C(p) of a point p∈l1n under dynamic updates of its coordinates, such that given sketches C(p) and C(q) one can estimate |p-q|1 up to a factor of (1+ε) with large probability. We obtain another sketch function C' which maps l1n into a normed space l1m (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 l1 norm we give an explicit embedding of l2n into llnO(log n) with distortion (1+1/nθ(1)) and a non-constructive embedding of l2n into l1O(n) with distortion (1+ε) such that the embedding can be represented using only O(n log2 n) bits (as opposed to at least n2 used by earlier methods)

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Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on

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