Succinct Sampling from Discrete Distributions

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Succinct Sampling from Discrete Distributions

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by Karl Bringmann , Kasper Green Larsen

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3 - 1 self

BibTeX

@MISC{Bringmann_succinctsampling,
    author = {Karl Bringmann and Kasper Green Larsen},
    title = {Succinct Sampling from Discrete Distributions},
    year = {}
}

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Abstract

We revisit the classic problem of sampling from a discrete distribution: Given n non-negative w-bit integers x1,..., xn, the task is to build a data structure that allows sampling i with probability proportional to xi. The classic solution is Walker’s alias method that takes, when implemented on a Word RAM, O(n) preprocessing time, O(1) expected query time for one sample, and n(w+2 lg n+o(1)) bits of space. Using the terminology of succinct data structures, this solution has redundancy 2n lg n + o(n) bits, i.e., it uses 2n lg n + o(n) bits in addition to the information theoretic minimum required for storing the input. In this paper, we study whether this space usage can be improved. In the systematic case, in which the input is read-only, we present a novel data structure using r + O(w) redundant

Keyphrases

discrete distribution word ram data structure walker alias method non-negative w-bit integer novel data structure probability proportional classic problem space usage classic solution succinct data structure query time preprocessing time information theoretic minimum systematic case

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