Efficient sampling of non-strict turnstile data streams

We study the problem of generating a large sample from a data stream of elements (i,v), where the sample consists of pairs (i,C_i) for C _i = ∑_{(i,v)∈stream} v. We consider strict turnstile streams and general non-strict turnstile streams, in which C_i may be negative. Our sample is useful for approximating both forward and inverse distribution statistics, within an additive error ε and provable success probability 1 - δ. Our sampling method improves by an order of magnitude the known processing time of each stream element, a crucial factor in data stream applications, thereby providing a feasible solution to the problem. For example, for a sample of size O(ε^-2 log(1/δ)) in non-strict streams, our solution requires O((loglog(1/ε))² + (loglog(1/δ))²) operations per stream element, whereas the best previous solution requires O(ε^-2 log²(1/δ)) evaluations of a fully independent hash function per element. We achieve this improvement by constructing an efficient K-elements recovery structure from which K elements can be extracted with probability 1 - δ. Our structure enables our sampling algorithm to run on distributed systems and extract statistics on the difference between streams.