Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Communication complexity
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An Approximate L1-Difference Algorithm for Massive Data Streams
SIAM Journal on Computing
An Information Statistics Approach to Data Stream and Communication Complexity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Fast Mining of Massive Tabular Data via Approximate Distance Computations
ICDE '02 Proceedings of the 18th International Conference on Data Engineering
Sketch-based change detection: methods, evaluation, and applications
Proceedings of the 3rd ACM SIGCOMM conference on Internet measurement
Optimal space lower bounds for all frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
A near-optimal algorithm for computing the entropy of a stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Estimators and tail bounds for dimension reduction in lα (0
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient and private distance approximation in the communication and streaming models
Efficient and private distance approximation in the communication and streaming models
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
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
Sketching and Streaming Entropy via Approximation Theory
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Numerical linear algebra in the streaming model
Proceedings of the forty-first annual ACM symposium on Theory of computing
A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
The Data Stream Space Complexity of Cascaded Norms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Bounded Independence Fools Halfspaces
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for sparse recovery
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the forty-second ACM symposium on Theory of computing
An optimal algorithm for the distinct elements problem
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Fast Manhattan sketches in data streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for sparse recovery
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
Near-optimal private approximation protocols via a black box transformation
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Subspace embeddings for the L1-norm with applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Lower bounds for testing computability by small width OBDDs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Periodicity and cyclic shifts via linear sketches
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Everywhere-tight information cost tradeoffs for augmented index
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Optimal bounds for Johnson-Lindenstrauss transforms and streaming problems with sub-constant error
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Estimating hybrid frequency moments of data streams
Journal of Combinatorial Optimization
Space-efficient estimation of statistics over sub-sampled streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Space-Efficient approximation scheme for circular earth mover distance
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Subconstant Error
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Tight lower bound for linear sketches of moments
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We settle the 1-pass space complexity of (1 ± ε)-approximating the Lp norm, for real p with 1 ≤ p ≤ 2, of a length-n vector updated in a length-m stream with updates to its coordinates. We assume the updates are integers in the range [--M, M]. In particular, we show the space required is Θ(ε-2 log(mM) + log log(ns)) bits. Our result also holds for 0 p Lp is not a norm in this case, it remains a well-defined function. Our upper bound improves upon previous algorithms of [Indyk, JACM '06] and [Li, SODA '08]. This improvement comes from showing an improved derandomization of the Lp sketch of Indyk by using k-wise independence for small k, as opposed to using the heavy hammer of a generic pseudorandom generator against space-bounded computation such as Nisan's PRG. Our lower bound improves upon previous work of [Alon-Matias-Szegedy, JCSS '99] and [Woodruff, SODA '04], and is based on showing a direct sum property for the 1-way communication of the gap-Hamming problem.