Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Quantifying knowledge complexity
Computational Complexity
Improved approximation algorithms for MAX SAT
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Secure Multiparty Computation of Approximations
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Practical privacy: the SuLQ framework
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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)
Private multiparty sampling and approximation of vector combinations
Theoretical Computer Science
Longest common subsequence as private search
Proceedings of the 8th ACM workshop on Privacy in the electronic society
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
Fast private norm estimation and heavy hitters
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Approximate privacy: foundations and quantification (extended abstract)
Proceedings of the 11th ACM conference on Electronic commerce
Differentially private combinatorial optimization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Near-optimal private approximation protocols via a black box transformation
Proceedings of the forty-third annual ACM symposium on Theory of computing
Polylogarithmic private approximations and efficient matching
TCC'06 Proceedings of the Third conference on Theory of Cryptography
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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The notion of private approximation was introduced recently by Feigenbaum, Fong, Strauss and Wright. Informally, a private approximation of a function f is another function F that approximates f in the usual sense, but does not yield any information on x other than what can be deduced from f(x). As such, F(x) is useful for private computation of f(x) (assuming that F can be computed more efficiently than f.In this work we examine the properties and limitations of this new notion. Specifically, we show that for many NP-hard problems, the privacy requirement precludes non-trivial approximation. This is the case even for problems that otherwise admit very good approximation (e.g., problems with PTAS). On the other hand, we show that slightly relaxing the privacy requirement, by means of leaking “just a few bits of informationrdquo; about x, again permits good approximation.