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Bringmann, Karl; Panagiotou, Konstantinos (2017): Efficient Sampling Methods for Discrete Distributions. In: Algorithmica, Vol. 79, No. 2: pp. 484-508
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Abstract

We study the fundamental problem of the exact and efficient generation of random values from a finite and discrete probability distribution. Suppose that we are given n distinct events with associated probabilities p(1,)...,p(n) First, we consider the problem of sampling from the distribution where the i-th event has probability proportional to p(i). Second, we study the problem of sampling a subset which includes the i-th event independently with probability . For both problems we present on two different classes of inputs-sorted and general probabilities-efficient data structures consisting of a preprocessing and a query algorithm. Varying the allotted preprocessing time yields a trade-off between preprocessing and query time, which we prove to be asymptotically optimal everywhere.