On the exact space complexity of sketching and streaming small norms

On the exact space complexity of sketching and streaming small norms (2010)

by Daniel M. Kane , Jelani Nelson , David P. Woodruff

Venue:	In SODA
Citations:	10 - 5 self

Datum	Value	Source
TITLE	On the exact space complexity of sketching and streaming small norms	INFERENCE
AUTHOR NAME	Daniel M. Kane	SVM HeaderParse 0.2
AUTHOR NAME	Jelani Nelson	SVM HeaderParse 0.2
AUTHOR NAME	David P. Woodruff	SVM HeaderParse 0.2
ABSTRACT	We settle the 1-pass space complexity of (1 ± ε)approximating the Lp norm, for real p with 1 ≤ p ≤ 2, of a length-n vector updated in a length-m stream with updates to its coordinates. We assume the updates are integers in the range [−M, M]. In particular, we show the space required is Θ(ε −2 log(mM) + log log(n)) bits. Our result also holds for 0 < p < 1; although Lp is not a norm in this case, it remains a well-defined function. Our upper bound improves upon previous algorithms of [Indyk, JACM ’06] and [Li, SODA ’08]. This improvement comes from showing an improved derandomization of the Lp sketch of Indyk by using k-wise independence for small k, as opposed to using the heavy hammer of a generic pseudorandom generator against space-bounded computation such as Nisan’s PRG. Our lower bound improves upon previous work of [Alon-Matias-Szegedy, JCSS ’99] and [Woodruff, SODA ’04], and is based on showing a direct sum property for the 1-way communication of the gap-Hamming problem. 1	SVM HeaderParse 0.2
YEAR	2010	INFERENCE
VENUE	In SODA	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
CITATIONS	40 found	ParsCit 1.0