In this overview paper we motivate the need for and research issues arising from a new model of data processing. In this model, data does not take the form of persistent relations, but rather arrives in multiple, continuous, rapid, time-varying data streams. In addition to reviewing past work relevant to data stream systems and current projects in the area, the paper explores topics in stream query languages, new requirements and challenges in query processing, and algorithmic issues. 1

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We present algorithms for computing frequency counts exceeding a user-specified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a user-specified parameter. Our algorithms can easily be deployed for streams of singleton items like those found in IP network monitoring. We can also handle streams of variable sized sets of items exemplified by a sequence of market basket transactions at a retail store. For such streams, we describe an optimized implementation to compute frequent itemsets in a single pass.

In many recent applications, data may take the form of continuous data streams, rather than finite stored data sets. Several aspects of data management need to be reconsidered in the presence of data streams, offering a new research direction for the database community. In this paper we focus primarily on the problem of query processing, specifically on how to define and evaluate continuous queries over data streams. We address semantic issues as well as efficiency concerns. Our main contributions are threefold. First, we specify a general and flexible architecture for query processing in the presence of data streams. Second, we use our basic architecture as a tool to clarify alternative semantics and processing techniques for continuous queries. The architecture also captures most previous work on continuous queries and data streams, as well as related concepts such as triggers and materialized views. Finally, we map out research topics in the area of query processing over data streams, showing where previous work is relevant and describing problems yet to be addressed.

between computers, and a resulting paradigm shift from centralized to highly distributed systems. With massive scale also comes massive instability, as node and link failures become the norm rather than the exception. For such highly volatile systems, decentralized gossip-based protocols are emerging as an approach to maintaining simplicity and scalability while achieving fault-tolerant information dissemination.

In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its coordinates, such that given sketches C(p) and C(q) one can estimate jp \Gamma qj 1 up to a factor of (1 + ffl) with large probability. This solves the main open problem of [10]. ffl we obtain another sketch function C 0 which maps l n 1 into a normed space l m 1 (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 l 1 norm ffl we give an explicit embedding of l n 2 into l n O(log n) 1 with distortion (1 + 1=n \Theta(1) ) and a nonconstructive embedding of l n 2 into l O(n) 1 with distortion (1 + ffl) such that the embedding can be represented using only O(n log 2 n) bits (as opposed to at least...

Abstract. We introduce a new sublinear space data structure—the Count-Min Sketch — for summarizing data streams. Our sketch allows fundamental queries in data stream summarization such as point, range, and inner product queries to be approximately answered very quickly; in addition, it can be applied to solve several important problems in data streams such as finding quantiles, frequent items, etc. The time and space bounds we show for using the CM sketch to solve these problems significantly improve those previously known — typically from 1/ε 2 to 1/ε in factor. 1

Abstract. We present a 1-pass algorithm for estimating the most frequent items in a data stream using very limited storage space. Our method relies on a novel data structure called a count sketch, which allows us to estimate the frequencies of all the items in the stream. Our algorithm achieves better space bounds than the previous best known algorithms for this problem for many natural distributions on the item frequencies. In addition, our algorithm leads directly to a 2-pass algorithm for the problem of estimating the items with the largest (absolute) change in frequency between two data streams. To our knowledge, this problem has not been previously studied in the literature. 1

Mayur Datar Aristides Gionis y Piotr Indyk z Rajeev Motwani x Abstract We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1's in the last N elements seen from the stream. We show that using O( 1 ffl log 2 N) bits of memory, we can estimate the number of 1's to within a factor of 1 + ffl. We also give a matching lower bound of \Omega\Gamma 1 ffl log 2 N) memory bits for any deterministic or randomized algorithms. We extend our scheme to maintain the sum of the last N positive integers. We provide matching upper and lower bounds for this more general problem as well. We apply our techniques to obtain efficient algorithms for the Lp norms (for p 2 [1; 2]) of vectors under the sliding window model. Using the algorithm for the basic counting problem, one can adapt many other techniques to work for the sliding window model, with a multiplicative overhead of O( 1 ffl log N) in memory and a 1 + ffl factor loss in accuracy. These include maintaining approximate histograms, hash tables, and statistics or aggregates such as sum and averages.

In the emerging area of sensor-based systems, a significant challenge is to develop scalable, fault-tolerant methods to extract useful information from the data the sensors collect. An approach to this data management problem is the use of sensor database systems, exemplified by TinyDB and Cougar, which allow users to perform aggregation queries such as MIN, COUNT and AVG on a sensor network. Due to power and range constraints, centralized approaches are generally impractical, so most systems use in-network aggregation to reduce network traffic. Also, aggregation strategies must provide fault-tolerance to address the issues of packet loss and node failures inherent in such a system. An unfortunate consequence of standard methods is that they typically introduce duplicate values, which must be accounted for to compute aggregates correctly. Another consequence of loss in the network is that exact aggregation is not possible in general. With this in mind, we investigate the use of approximate in-network aggregation using small sketches. Our contributions are as follows: 1) we generalize well known duplicateinsensitive sketches for approximating COUNT to handle SUM (and by extension, AVG and other aggregates), 2) we present and analyze methods for using sketches to produce accurate results with low communication and computation overhead (even on low-powered CPUs with little storage and no floating point operations), and 3) we present an extensive experimental validation of our methods. 1