Communication complexity
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Private approximation of NP-hard functions
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Communication preserving protocols for secure function evaluation
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Space lower bounds for distance approximation in the data stream model
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
An Approximate L1-Difference Algorithm for Massive Data Streams
SIAM Journal on Computing
Finding Frequent Items in Data Streams
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Comparing Data Streams Using Hamming Norms (How to Zero In)
IEEE Transactions on Knowledge and Data Engineering
Tabulation based 4-universal hashing with applications to second moment estimation
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Improved range-summable random variable construction algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An improved data stream summary: the count-min sketch and its applications
Journal of Algorithms
Summarizing and mining inverse distributions on data streams via dynamic inverse sampling
VLDB '05 Proceedings of the 31st international conference on Very large data bases
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
Oblivious Polynomial Evaluation
SIAM Journal on Computing
Private approximation of search problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Secure multiparty computation of approximations
ACM Transactions on Algorithms (TALG)
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Coresets forWeighted Facilities and Their Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Sampling-based dimension reduction for subspace approximation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Efficient subspace approximation algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Range-Efficient Counting of Distinct Elements in a Massive Data Stream
SIAM Journal on Computing
Estimators and tail bounds for dimension reduction in lα (0
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Declaring independence via the sketching of sketches
Proceedings of the nineteenth 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
Two improved range-efficient algorithms for F0 estimation
Theoretical Computer Science
Private multiparty sampling and approximation of vector combinations
Theoretical Computer Science
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Private Approximation of Clustering and Vertex Cover
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
Efficient Sketches for Earth-Mover Distance, with Applications
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Computationally private information retrieval with polylogarithmic communication
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Differential privacy: a survey of results
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Fast private norm estimation and heavy hitters
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Proceedings of the forty-second ACM symposium on Theory of computing
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
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
Sublinear Optimization for Machine Learning
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Estimating entropy and entropy norm on data streams
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Single-database private information retrieval with constant communication rate
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Polylogarithmic private approximations and efficient matching
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Subconstant Error
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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We show the following transformation: any two-party protocol for outputting a (1+ε)-approximation to f(x,y) = ∑j=1n g(xj, yj) with probability at least 2/3, for any non-negative efficienty computable function g, can be transformed into a two-party private approximation protocol with only a polylogarithmic factor loss in communication, computation, and round complexity. In general it is insufficient to use secure function evaluation or fully homomorphic encryption on a standard, non-private protocol for approximating f. This is because the approximation may reveal information about x and y that does not follow from f(x,y). Applying our transformation and variations of it, we obtain near-optimal private approximation protocols for a wide range of problems in the data stream literature for which previously nothing was known. We give near-optimal private approximation protocols for the lp-distance for every p ≥ 0, for the heavy hitters and importance sampling problems with respect to any lp-norm, for the max-dominance and other dominant lp-norms, for the distinct summation problem, for entropy, for cascaded frequency moments, for subspace approximation and block sampling, and for measuring independence of datasets. Using a result for data streams, we obtain private approximation protocols with polylogarithmic communication for every non-decreasing and symmetric function g(xj,yj) = h(xj-yj) with at most quadratic growth. If the original (non-private) protocol is a simultaneous protocol, e.g., a sketching algorithm, then our only cryptographic assumption is efficient symmetric computationally-private information retrieval; otherwise it is fully homomorphic encryption. For all but one of these problems, the original protocol is a sketching algorithm. Our protocols generalize straightforwardly to more than two parties.