STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Construction of extractors using pseudo-random generators (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Extracting all the randomness and reducing the error in Trevisan's extractors
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On recycling the randomness of states in space bounded computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Sampling algorithms: lower bounds and applications
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Sparse and limited wavelength conversion in all-optical tree networks
Theoretical Computer Science
Lower bounds for dynamic algebraic problems
Information and Computation
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
Bandwidth allocation in WDM tree networks
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Recent Advances in Wavelength Routing
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
Error Reduction for Extractors
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Reusable cryptographic fuzzy extractors
Proceedings of the 11th ACM conference on Computer and communications security
On Pseudorandom Generators with Linear Stretch in NC0
Computational Complexity
Lower bounds for dynamic algebraic problems
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Noise-resilient group testing: limitations and constructions
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Cryptography in constant parallel time
Cryptography in constant parallel time
On the error parameter of dispersers
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
On hardness amplification of one-way functions
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Entropic security and the encryption of high entropy messages
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
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We show that the minimum size of a depth-two N-superconcentrator is /spl Theta/(Nlog/sup 2/N/loglogN). Before this work, optimal bounds were known for all depths except two. For the upper bound, we build superconcentrators by putting together a small number of disperser graphs; these disperser graphs are obtained using a probabilistic argument. We present two different methods for showing lower bounds. First, we show that superconcentrators contain several disjoint disperser graphs. When combined with the lower bound for disperser graphs due to Kovari, Sos and Turan, this gives an almost optimal lower bound of /spl Omega/(N(log N/loglog N)/sup 2/) on the size of N-superconcentrators. The second method, based on the work of Hansel (1964), gives the optimal lower bound. The method of the Kovari, Sos and Turan can be extended to give tight lower bounds for extractors, both in terms of the number of truly random bits needed to extract one additional bit and in terms of the unavoidable entropy loss in the system. If the input is an n-bit source with min-entropy /spl kappa/ and the output is required to be within a distance of E from uniform distribution, then to extract even a constant number of additional bits, one must invest at least log(n-/spl kappa/)+2 log(1//spl epsiv/)-O(1) truly random bits; to obtain m output bits one must invest at least m-/spl kappa/+2 log(1//spl epsiv/)-O(1). Thus, there is a loss of 2 log(1//spl epsiv/) bits during the extraction. Interestingly in the case of dispersers this loss in entropy is only about loglog(1//spl epsiv/).