Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Revealing information while preserving privacy
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Limiting privacy breaches in privacy preserving data mining
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating extent measures of points
Journal of the ACM (JACM)
High-Dimensional Shape Fitting in Linear Time
Discrete & Computational Geometry
Coresets in dynamic geometric data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Smaller coresets for k-median and k-means clustering
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Practical privacy: the SuLQ framework
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Subgradient and sampling algorithms for l1 regression
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
SIAM Journal on Computing
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Privacy via pseudorandom sketches
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Coresets forWeighted Facilities and Their Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Sublinear-time approximation algorithms for clustering via random sampling
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Bi-criteria linear-time approximations for generalized k-mean/median/center
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Smooth sensitivity and sampling in private data analysis
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The price of privacy and the limits of LP decoding
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Privacy, accuracy, and consistency too: a holistic solution to contingency table release
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The boundary between privacy and utility in data publishing
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Mechanism Design via Differential Privacy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A learning theory approach to non-interactive database privacy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Estimating clustering indexes in data streams
ESA'07 Proceedings of the 15th annual European conference on Algorithms
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Our data, ourselves: privacy via distributed noise generation
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
On the complexity of differentially private data release: efficient algorithms and hardness results
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the geometry of differential privacy
Proceedings of the forty-second ACM symposium on Theory of computing
Data mining with differential privacy
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Differentially private combinatorial optimization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Differentially private data release through multidimensional partitioning
SDM'10 Proceedings of the 7th VLDB conference on Secure data management
Differentially private data cubes: optimizing noise sources and consistency
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
iReduct: differential privacy with reduced relative errors
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
The application of differential privacy to health data
Proceedings of the 2012 Joint EDBT/ICDT Workshops
Functional mechanism: regression analysis under differential privacy
Proceedings of the VLDB Endowment
Adaptive differentially private histogram of low-dimensional data
PETS'12 Proceedings of the 12th international conference on Privacy Enhancing Technologies
Is privacy compatible with truthfulness?
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Efficient and accurate strategies for differentially-private sliding window queries
Proceedings of the 16th International Conference on Extending Database Technology
Learning Big (Image) Data via Coresets for Dictionaries
Journal of Mathematical Imaging and Vision
Distributed and Parallel Databases
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A coreset of a point set P is a small weighted set of points that captures some geometric properties of $P$. Coresets have found use in a vast host of geometric settings. We forge a link between coresets, and differentially private sanitizations that can answer any number of queries without compromising privacy. We define the notion of private coresets, which are simultaneously both coresets and differentially private, and show how they may be constructed. We first show that the existence of a small coreset with low generalized sensitivity (i.e., replacing a single point in the original point set slightly affects the quality of the coreset) implies (in an inefficient manner) the existence of a private coreset for the same queries. This greatly extends the works of Blum, Ligett, and Roth [STOC 2008] and McSherry and Talwar [FOCS 2007]. We also give an efficient algorithm to compute private coresets for k-median and k-mean queries in Red, immediately implying efficient differentially private sanitizations for such queries. Following McSherry and Talwar, this construction also gives efficient coalition proof (approximately dominant strategy) mechanisms for location problems. Unlike coresets which only have a multiplicative approximation factor, we prove that private coresets must have an additive error. We present a new technique for showing lower bounds on this error.