@techreport{TD:100281, att_abstract={{From a high volume stream of weighted items, we want to maintain a generic sample of a certain limited size k that we can later use to estimate the total weight of arbitrary subsets. This is the classic context of on-line reservoir sampling, thinking of the generic sample as a reservoir. We present an efficient reservoir sampling scheme, VAROPTk, that dominates all previous schemes in terms of estimation quality. VAROPTk provides variance optimal unbiased estimation of subset sums. More precisely, if we have seen n items of the stream, then for any subset size m, our scheme based on k samples minimizes the average variance over all subsets of size m. In fact, the optimality is against any off-line scheme with k samples tailored for the concrete set of items seen. In addition to optimal average variance, our scheme provides tighter worst-case bounds on the variance of particular subsets than previously possible. It is efficient, handling each new item of the stream in O(log k) time. Finally, it is particularly well suited for combination of samples from different streams in a distributed setting. }}, att_authors={ec1458, nd1321, cl9862, mt2514}, att_categories={C_CCF.6, C_CCF.1, C_CCF.9}, att_copyright={{SIAM (Society fir Industrial and Applied Mathematics)}}, att_copyright_notice={{The definitive version was published in SIAM Journal on Computing. {{, 2011-06-01}}}}, att_donotupload={}, att_private={false}, att_projects={}, att_tags={Sampling, Estimation, Streaming, Variance Minimization}, att_techdoc={true}, att_techdoc_key={TD:100281}, att_url={http://web1.research.att.com:81/techdocs_downloads/TD:100281_DS1_2010-11-10T16:56:51.555Z.pdf}, author={Edith Cohen and Nicholas Duffield and Carsten Lund and Mikkel Thorup and Haim Kaplan}, institution={{SIAM Journal on Computing}}, month={June}, title={{Efficient stream sampling for variance-optimal estimation of subset sums}}, year=2011, }