This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we call the Fast Loaded Dice Roller (FLDR), is highly efficient in both space and time: (i) the size of the sampler is guaranteed to be linear in the number of bits needed to encode the input distribution; and (ii) the expected number of bits of entropy it consumes per sample is at most 6 bits more than the information-theoretically optimal rate. We present fast implementations of the linear-time preprocessing and near-optimal sampling algorithms using unsigned integer arithmetic. Empirical evaluations on a broad set of probability distributions establish that FLDR is 2x-10x faster in both preprocessing and sampling than multiple baseline algorithms, including the widely-used alias and interval samplers. It also uses up to 10000x less space than the information-theoretically optimal sampler, at the expense of less than 1.5x runtime overhead.

中文翻译：

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快速加载骰子滚轮：离散概率分布的近乎最优精确采样器

本文介绍了一种新算法，用于解决使用独立且无偏的随机抛硬币源从离散概率分布生成随机整数的基本问题。我们证明了这种称为快速加载骰子滚轮 (FLDR) 的算法在空间和时间上都非常高效：(i) 采样器的大小保证与编码输入所需的位数成线性关系分配; (ii) 每个样本消耗的熵的预期位数最多比信息理论上的最佳速率多 6 位。我们使用无符号整数算法快速实现线性时间预处理和接近最优的采样算法。对大量概率分布的实证评估表明，FLDR 在预处理和采样方面比多种基线算法（包括广泛使用的别名和间隔采样器）快 2 到 10 倍。它还使用比信息理论上最佳采样器少 10000 倍的空间，但运行时开销不到 1.5 倍。