TY - CHAP

T1 - A sample of samplers

T2 - A computational perspective on sampling

AU - Goldreich, Oded

PY - 2011

Y1 - 2011

N2 - 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∑x∈ {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 •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.

AB - 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∑x∈ {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 •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.

UR - http://www.scopus.com/inward/record.url?scp=84857521681&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-642-22670-0_24

DO - https://doi.org/10.1007/978-3-642-22670-0_24

M3 - فصل

SN - 9783642226694

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 302

EP - 332

BT - Studies in Complexity and Cryptography

A2 - Goldreich, Oded

ER -