The complexity of generating an exponentially distributed variate
Journal of Algorithms
Trie partitioning process: limiting distributions
CAAP '86 Proceedings of the 11th colloquium on trees in algebra and programming
Discrete Mathematics
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Mellin transforms and asymptotics: harmonic sums
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
On the rapid computation of various polylogarithmic constants
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Analytic variations on bucket selection and sorting
Acta Informatica
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Boltzmann Samplers for the Random Generation of Combinatorial Structures
Combinatorics, Probability and Computing
New Coins From Old: Computing With Unknown Bias
Combinatorica
On the convergence of Newton's method for monotone systems of polynomial equations
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Analytic Combinatorics
Succinct sampling from discrete distributions
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Exact and efficient generation of geometric random variates and random graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Non-redundant random generation algorithms for weighted context-free grammars
Theoretical Computer Science
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The well-know needle experiment of Buffon can be regarded as an analog (i.e., continuous) device that stochastically "computes" the number 2/π = 0.63661, which is the experiment's probability of success. Generalizing the experiment and simplifying the computational framework, we consider probability distributions, which can be produced perfectly, from a discrete source of unbiased coin flips. We describe and analyse a few simple Buffon machines that generate geometric, Poisson, and logarithmic-series distributions. We provide human-accessible Buffon machines, which require a dozen coin flips or less, on average, and produce experiments whose probabilities of success are expressible in terms of numbers such as π, exp(−1), log2, √3, cos(1/4), ζ(5). Generally, we develop a collection of constructions based on simple probabilistic mechanisms that enable one to design Buffon experiments involving compositions of exponentials and logarithms, polylogarithms, direct and inverse trigonometric functions, algebraic and hypergeometric functions, as well as functions defined by integrals, such as the Gaussian error function.