A Sample of Samplers: A Computational Perspective on Sampling

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} → [0, 1], we wish to estimate 2 Px∈{0,1}n f(x) upto an additive error of ǫ. 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(ǫ · log(1/δ)) queries and uses n+O(log(1/ǫ)) +O(log(1/δ)) coin tosses, both complexities being very close to the corresponding lower bounds.