Asymptotic methods in statistical theory
Asymptotic methods in statistical theory
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
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
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of massive data set computations
The complexity of massive data set computations
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
Estimators and tail bounds for dimension reduction in lα (0
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On Estimating Frequency Moments of Data Streams
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Introduction to Nonparametric Estimation
Introduction to Nonparametric Estimation
Fast Manhattan sketches in data streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the exact space complexity of sketching and streaming small norms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds for Lp samplers, finding duplicates in streams, and related problems
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Streaming Algorithms via Precision Sampling
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
The problem of estimating frequency moments of a data stream has attracted a lot of attention since the onset of streaming algorithms [AMS99]. While the space complexity for approximately computing the pth moment, for p∈(0,2] has been settled [KNW10], for p2 the exact complexity remains open. For p2 the current best algorithm uses O(n1−2/plogn) words of space [AKO11,BO10], whereas the lower bound is of Ω(n1−2/p) [BJKS04]. In this paper, we show a tight lower bound of Ω(n1−2/plogn) words for the class of algorithms based on linear sketches, which store only a sketch Ax of input vector x and some (possibly randomized) matrix A. We note that all known algorithms for this problem are linear sketches.