Explicit expanders and the Ramanujan conjectures
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Expanders, randomness, or time versus space
Proc. of the conference on Structure in complexity theory
Deterministic simulation in LOGSPACE
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
On the power of two-point based sampling
Journal of Complexity
Lower bounds for sampling algorithms for estimating the average
Information Processing Letters
Eigenvalues and expansion of regular graphs
Journal of the ACM (JACM)
When Hamming meets Euclid: the approximability of geometric TSP and MST (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Tiny families of functions with random properties: a quality-size trade-off for hashing
Proceedings of the workshop on Randomized algorithms and computation
Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
Sampling algorithms: lower bounds and applications
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Shift Register Sequences
Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Dispersers, deterministic amplification, and weak random sources
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Security preserving amplification of hardness
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Randomness in interactive proofs
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Randomness-efficient oblivious sampling
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
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We consider the problem of estimating the average of a huge set of values. That is, given oracle access to an arbitrary function f : {0, 1}n → [0, 1], we wish to estimate 2-n Σx∈{0,1}n f(x) upto an additive error of ε. We are allowed to employ a randomized algorithm that may err with probability at most δ. We survey known algorithms for this problem and focus on the ideas underlying their construction. In particular, we present an algorithm that makes O(ε-2 ċ log(1/δ)) queries and uses n + O(log(1/ε)) + O(log(1/δ)) coin tosses, both complexities being very close to the corresponding lower bounds.