CR-precis: A Deterministic Summary Structure for Update Data Streams

Abstract

Abstract. We present the first deterministic sub-linear space algorithms for a number of fundamental problems over update data streams, such as, (a) point queries, (b) range-sum queries, (c) finding approximate frequent items, (d) finding approximate quantiles, (e) finding approximate hierarchical heavy hitters, (f) estimating inner-products, (g) constructing near-optimal B-bucket histograms, (h) estimating entropy of data streams, etc.. We also present new lower bound results for several problems over update data streams.

Quantiles over data streams: experimental comparisons, new analyses, and further improvements

“…Therefore, all turnstile algorithms work only for a fixed universe, and are mostly randomized algorithms. Deterministic algorithms for the fixed universe model have been provided: Ganguly and Majumder describe an algorithm which uses O( 1 ε 2 log 5 u log( log u ε )) space [12]. The high dependency on 1 ε and log u is not considered practical.…”

“…In the past 35 years, this problem has received particular attention in the streaming model, i.e., the data elements arrive one by one in a streaming fashion, and the algorithm only has lim-ited memory to work with. There have been numerous algorithms proposed in this setting, using a variety of different techniques and offering different performance guarantees [23,15,21,22,13,7,12,18,27]. In addition, there have been many studies on variations and extensions of the problem, such as computing quantiles over sliding windows [3], over distributed data [26,1,16,17], continuous monitoring of quantiles [9,30], biased quantiles [10], computing quantiles using GPUs [14], etc.…”

Estimating hybrid frequency moments of data streams

“…Alon, Matias and Szegedy [1] present a seminal randomized sketch technique for -approximation of 2 ( ) in the data streaming model using space ( −2 log 1 ( )) bits. Using the techniques of [1], it is easily shown that deterministically estimating ( ) for any real ≥ 0 requires ( ) space [11]. Hence, work in the area of sub-linear space estimation of moments has considered only randomized algorithms.…”

Estimating Hybrid Frequency Moments of Data Streams

“…We will say that a randomized algorithm computes an -approximation to a real valued quantity , provided, it returnsˆ such that |ˆ − | < , with probability ≥ Alon, Matias and Szegedy [1] present a seminal randomized sketch technique for -approximation of 2 ( ) in the data streaming model using space ( −2 log 1 ( )) bits. Using the techniques of [1], it is easily shown that deterministically estimating ( ) for any real ≥ 0 requires ( ) space [11]. Hence, work in the area of sub-linear space estimation of moments has considered only randomized algorithms.…”