Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Expanders that beat the eigenvalue bound: explicit construction and applications
STOC '93 Proceedings of the twenty-fifth 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
Journal of the ACM (JACM)
List decoding algorithms for certain concatenated codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Membership in Constant Time and Minimum Space
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Deterministic load balancing and dictionaries in the parallel disk model
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Rearrangeable and nonblocking [w, f] -distributors
IEEE/ACM Transactions on Networking (TON)
Applications of a Splitting Trick
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Data structures for storing small sets in the bitprobe model
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Pseudo-random graphs and bit probe schemes with one-sided error
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Reconstructive dispersers and hitting set generators
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
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We deal with the problem of storing a set of K elements that are taken from a large universe of size N, such that membership in the set can be determined with high probability by looking at just one bit of the representation. Buhrman et al. show an explicit construction with about K2 log N storing bits. We show an explicit construction with about K1+o(1) storing bits, that gets closer to the optimal K log N bound.Our technique is of independent interest. Buhrman et al. show a non-explicit optimal (up to constant factors) construction that is based on the existence of certain good unbalanced expanders. To make the construction explicit one needs to be able to explicitly 'encode' and 'decode' such expanding graphs. We generalize the notion of loss-less condensers of Ta-Shma et al. [Proc. 33rd Annual ACM Symposium on Theory of Computing, 2001, pp. 143-152] and build such graphs. We further show how to efficiently decode such graphs using an observation from Ta-Shma and Znckerman [Manuscript, 2001] about Trevisan's extractor.