Random sampling with a reservoir
ACM Transactions on Mathematical Software (TOMS)
Elements of information theory
Elements of information theory
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
A small approximately min-wise independent family of hash functions
Journal of Algorithms
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling from a moving window over streaming data
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining stream statistics over sliding windows: (extended abstract)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed streams algorithms for sliding windows
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Counting Distinct Elements in a Data Stream
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Tight Lower Bounds for the Distinct Elements Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Optimal space lower bounds for all frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate counts and quantiles over sliding windows
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Space efficient mining of multigraph streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An improved data stream summary: the count-min sketch and its applications
Journal of Algorithms
Profiling internet backbone traffic: behavior models and applications
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications
The Complexity of Approximating the Entropy
SIAM Journal on Computing
Entropy Based Worm and Anomaly Detection in Fast IP Networks
WETICE '05 Proceedings of the 14th IEEE International Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprise
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On graph problems in a semi-streaming model
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Data streaming algorithms for estimating entropy of network traffic
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Detecting anomalies in network traffic using maximum entropy estimation
IMC '05 Proceedings of the 5th ACM SIGCOMM conference on Internet Measurement
Estimating entropy over data streams
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A near-optimal algorithm for computing the entropy of a stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Sketching and Streaming Entropy via Approximation Theory
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Estimating entropy and entropy norm on data streams
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Testing Symmetric Properties of Distributions
SIAM Journal on Computing
Testing Closeness of Discrete Distributions
Journal of the ACM (JACM)
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We describe a simple algorithm for approximating the empirical entropy of a stream of m values up to a multiplicative factor of (1+ε) using a single pass, O(ε−2 log (δ−1) log m) words of space, and O(log ε−1 + log log δ−1 + log log m) processing time per item in the stream. Our algorithm is based upon a novel extension of a method introduced by Alon et al. [1999]. This improves over previous work on this problem. We show a space lower bound of Ω(ε−2/log2 (ε−1)), demonstrating that our algorithm is near-optimal in terms of its dependency on ε. We show that generalizing to multiplicative-approximation of the kth-order entropy requires close to linear space for k≥1. In contrast we show that additive-approximation is possible in a single pass using only poly-logarithmic space. Lastly, we show how to compute a multiplicative approximation to the entropy of a random walk on an undirected graph.