A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Making zero-knowledge provers efficient
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
On limited nondeterminism and the complexity of the V-C dimension
Journal of Computer and System Sciences
Computational Complexity and Knowledge Complexity
SIAM Journal on Computing
Quantifying knowledge complexity
Computational Complexity
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh 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
Some optimal inapproximability results
Journal of the ACM (JACM)
Secure computation of the mean and related statistics
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Polylogarithmic private approximations and efficient matching
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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
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Many approximation algorithms have been presented in the last decades for hard search problems. The focus of this paper is on cryptographic applications, where it is desired to design algorithms which do not leak unnecessary information. Specifically, we are interested in private approximation algorithms -- efficient algorithms whose output does not leak information not implied by the optimal solutions to the search problems. Privacy requirements add constraints on the approximation algorithms; in particular, known approximation algorithms usually leak a lot of information.For functions, [Feigenbaum et al., ICALP 2001] presented a natural requirement that a private algorithm should not leak information not implied by the original function. Generalizing this requirement to search problems is not straightforward as an input may have many different outputs. We present a new definition that captures a minimal privacy requirement from such algorithms -- applied to an input instance, it should not leak any information that is not implied by its collection of exact solutions. Although our privacy requirement seems minimal, we show that for well studied problems, as vertex cover and 3SAT, private approximation algorithms are unlikely to exist even for poor approximation ratios. Similar to [Halevi et al., STOC 2001], we define a relaxed notion of approximation algorithms that leak (little) information, and demonstrate the applicability of this notion by showing near optimal approximation algorithms for 3SAT that leak little information.