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 . We consider the problem of sampling a subset, which includes the ith event independently with probability p i , and the problem of sampling from the distribution, where the ith event has a probability proportional to p i . For both problems, we present on two different classes of inputs – sorted and general probabilities – efficient preprocessing algorithms that allow for asymptotically optimal querying, and prove almost matching lower bounds for their complexity.
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Bringmann, K., Panagiotou, K. (2012). Efficient Sampling Methods for Discrete Distributions. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_12
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DOI: https://doi.org/10.1007/978-3-642-31594-7_12
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