Global min-cuts in RNC, and other ramifications of a simple min-out algorithm
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Private approximation of NP-hard functions
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Local Search Heuristics for k-Median and Facility Location Problems
SIAM Journal on Computing
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
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)
Smooth sensitivity and sampling in private data analysis
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Distributed Private Data Analysis: Simultaneously Solving How and What
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On the Hardness of Being Truthful
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Privacy: Theory meets Practice on the Map
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Private approximation of clustering and vertex cover
TCC'07 Proceedings of the 4th conference on Theory of cryptography
How should we solve search problems privately?
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Differential privacy: a survey of results
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
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
Polylogarithmic private approximations and efficient matching
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Winner-imposing strategyproof mechanisms for multiple facility location games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Pan-private algorithms via statistics on sketches
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Differentially Private Empirical Risk Minimization
The Journal of Machine Learning Research
Optimal lower bounds for universal and differentially private steiner trees and TSPs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Sharing graphs using differentially private graph models
Proceedings of the 2011 ACM SIGCOMM conference on Internet measurement conference
Probabilistic relational reasoning for differential privacy
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The power of the dinur-nissim algorithm: breaking privacy of statistical and graph databases
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Beating randomized response on incoherent matrices
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Buying private data at auction: the sensitive surveyor's problem
ACM SIGecom Exchanges
Distributed private heavy hitters
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Differentially private projected histograms: construction and use for prediction
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II
Linear dependent types for differential privacy
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Winner-imposing strategyproof mechanisms for multiple Facility Location games
Theoretical Computer Science
Take it or leave it: running a survey when privacy comes at a cost
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Probabilistic Relational Reasoning for Differential Privacy
ACM Transactions on Programming Languages and Systems (TOPLAS)
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Consider the following problem: given a metric space, some of whose points are "clients," select a set of at most k facility locations to minimize the average distance from the clients to their nearest facility. This is just the well-studied k-median problem, for which many approximation algorithms and hardness results are known. Note that the objective function encourages opening facilities in areas where there are many clients, and given a solution, it is often possible to get a good idea of where the clients are located. This raises the following quandary: what if the locations of the clients are sensitive information that we would like to keep private? Is it even possible to design good algorithms for this problem that preserve the privacy of the clients? In this paper, we initiate a systematic study of algorithms for discrete optimization problems in the framework of differential privacy (which formalizes the idea of protecting the privacy of individual input elements). We show that many such problems indeed have good approximation algorithms that preserve differential privacy; this is even in cases where it is impossible to preserve cryptographic definitions of privacy while computing any non-trivial approximation to even the value of an optimal solution, let alone the entire solution. Apart from the k-median problem, we consider the problems of vertex and set cover, min-cut, k-median, facility location, and Steiner tree, and give approximation algorithms and lower bounds for these problems. We also consider the recently introduced sub-modular maximization problem, "Combinatorial Public Projects" (CPP), shown by Papadimitriou et al. [28] to be inapproximable to subpolynomial multiplicative factors by any efficient and truthful algorithm. We give a differentially private (and hence approximately truthful) algorithm that achieves a logarithmic additive approximation.