Elements of information theory
Elements of information theory
On the distributional complexity of disjointness
Theoretical Computer Science
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Communication complexity
An Approximate L1-Difference Algorithm for Massive Data Streams
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Information Theory Methods in Communication Complexity
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An improved data stream algorithm for frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Finding frequent items in data streams
Theoretical Computer Science - Special issue on automata, languages and programming
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
Buffering in query evaluation over XML streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Earth mover distance over high-dimensional spaces
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sketching information divergences
Machine Learning
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Revisiting the Direct Sum Theorem and Space Lower Bounds in Random Order Streams
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Hellinger Strikes Back: A Note on the Multi-party Information Complexity of AND
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Sketching information divergences
COLT'07 Proceedings of the 20th annual conference on Learning theory
Communication lower bounds via the chromatic number
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Recognizing well-parenthesized expressions in the streaming model
Proceedings of the forty-second ACM symposium on Theory of computing
Information complexity: a tutorial
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
ACM SIGACT News
The Computational Hardness of Estimating Edit Distance
SIAM Journal on Computing
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
The Value of Multiple Read/Write Streams for Approximating Frequency Moments
ACM Transactions on Computation Theory (TOCT)
SIAM Journal on Computing
Finding longest increasing and common subsequences in streaming data
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On approximation algorithms for data mining applications
Efficient Approximation and Online Algorithms
Streaming algorithms measured in terms of the computed quantity
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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(MATH) We consider the problem of approximating the distance of two d-dimensional vectors x and y in the data stream model. In this model, the 2d coordinates are presented as a "stream" of data in some arbitrary order, where each data item includes the index and value of some coordinate and a bit that identifies the vector (x or y) to which it belongs. The goal is to minimize the amount of memory needed to approximate the distance. For the case of Lp-distance with p &egr; [1,2], there are good approximation algorithms that run in polylogarithmic space in d (here we assume that each coordinate is an integer with O(log d) bits). Here we prove that they do not exist for pρ2. In particular, we prove an optimal approximation-space tradeoff of approximating L&infty; distance of two vectors. We show that any randomized algorithm that approximates L&infty; distance of two length d vectors within factor of d&dgr; requires ω(d1—4&dgr;) space. As a consequence we show that for pρ2/(1—4&dgr;), any randomized algorithm that approximate Lp distance of two length d vectors within a factor d&dgr; requires ω(d 1— 2p—4&dgr;) space.The lower bound follows from a lower bound on the two-party one-round communication complexity of this problem. This lower bound is proved using a combination of information theory and Fourier analysis.