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Abstract: We consider the problem of estimating the average of a huge set of values. That is, given oracle access to an arbitrary function f : f0; 1g n 7! [0; 1], we need to estimate 2 \Gamman P x2f0;1g n f(x) upto an additive error of ffl. We are allowed to employ a randomized algorithm which may err with probability at most ffi . We survey known algorithms for this problem and focus on the ideas underlying their construction. In particular, we present an algorithm which makes O(ffl \Gamma2... (Update)
Context of citations to this paper: More
...on [n] with high probability. Such sampling procedures are known as averaging (or oblivious) samplers, and have been studied extensively [BR94, CEG95, Zuc97, Gol97]. Our definition di#ers slightly from the standard definition, to allow us to obtain some savings in parameters...
.... to a number of other important and widely studied objects, such as hash functions [9] expander graphs [14, 28, 18, 23, 4] samplers [7, 30], pseudorandom generators [26] and error correcting codes [26, 25, 24] In addition, extractors have been found to have a vast and ever...
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1.7: A Sample of Samplers: A Computational Perspective on Sampling - Goldreich (1997) (Correct)
0.8: Tiny Families of Functions with Random Properties: A.. - Goldreich (1994) (Correct)
0.3: Computing With Very Weak Random Sources - Srinivasan, Zuckerman (Correct)
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0.3: Candidate One-Way Functions Based on Expander Graphs - Goldreich (2000) (Correct)
0.1: Probabilistic Proof Systems - Part I - Vadhan (2000) (Correct)
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7: Simulating BPP Using a General Weak Random Source - Zuckerman - 1991
7: Randomness is Linear in Space - Nisan, Zuckerman - 1993
6: Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Co.. - Chor, Goldreich - 1988
BibTeX entry: (Update)
Goldreich O. (1997), "A Sample of Samplers: A Computational Perspective on Sampling", ECCC, TR97-20. http://citeseer.ist.psu.edu/article/goldreich97sample.html More
@article{ goldreich97sample,
author = "Oded Goldreich",
title = "A Sample of Samplers - A Computational Perspective on Sampling (survey)",
journal = "Electronic Colloquium on Computational Complexity (ECCC)",
volume = "4",
number = "020",
year = "1997",
url = "citeseer.ist.psu.edu/article/goldreich97sample.html" }
Citations (may not include all citations):957 The Probabilistic Method (context) - Alon, Spencer - 1992
358 Universal Classes of Hash Functions (context) - Carter, Wegman - 1979
122 How to Recycle Random Bits - Impagliazzo, Zuckerman - 1989
120 Unbiased Bits from Sources of Weak Randomness and Probabilis.. - Chor, Goldreich - 1988
88 Deterministic Simulation in LogSpace (context) - Ajtai, Komlos et al. - 1987
70 the Power of Two--Point Based Sampling - Chor, Goldreich - 1989
58 Construction of Asymptotically Good, Low-Rate Error-Correcti.. (context) - Alon, Bruck et al. - 1992
40 Tiny Families of Functions with Random Properties: A Quality.. - Goldreich, Wigderson - 1994
40 Explicit Expanders and the Ramanujan Conjectures (context) - Lubotzky, Phillips et al. - 1986
36 Security Preserving Amplification of Hardness - Goldreich, Impagliazzo et al. - 1990
30 Isoperimetric Inequalities for Graphs and Superconcentrators (context) - Alon, Milman - 1985
28 Extracting randomness: how and why (a survey (context) - Nisan - 1996
27 When Hamming meets Euclid: The Approximability of Geometric .. - Trevisan - 1997
20 Eigenvalues and Expansion of Regular Graphs - Kahale - 1995
20 Lower Bounds for Sampling Algorithms for Estimating the Aver.. - Canetti, Even et al. - 1995
19 Explicit Constructions of Linear Size Superconcentrators (context) - Gaber, Galil - 1981
16 Randomness-efficient oblivious sampling (context) - Bellare, Rompel - 1994
15 A Time-Randomness Tradeoff (context) - Karp, Pippinger et al. - 1985
10 Dispensers, Deterministic Amplification, and Weak Random Sou.. (context) - Cohen, Wigderson - 1989
9 Expanders, Randomness or Time vs Space (context) - Sipser - 1986
8 Eigenvalues, Geometric Expanders, Sorting in Rounds and Rams.. (context) - Alon - 1986
7 Randomness-Optimal Sampling, Extractors, and Constructive Le.. (context) - Zuckerman - 1996
4 Random Polynomial Time Equal to Semi-Random Polynomial Time (context) - Vazirani, Vazirani - 1985
4 available from http://theory (context) - Bellare, Goldreich et al. - 1997
4 Weak Random Sources, Hitting Sets, and BPP Simulation - Andreev, Clementi et al. - 1997
The graph only includes citing articles where the year of publication is known.
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