Related papers: Optimal Discrete Uniform Generation from Coin Flip…
An algorithm is presented which, with optimal efficiency, solves the problem of uniform random generation of distribution functions for an n-valued random variable.
This article presents an efficient algorithm to generate a discrete uniform distribution on a set of $p$ elements using a biased random source for $p$ prime. The algorithm generalizes Von Neumann's method and improves computational…
For any discrete probability distributions with bounded entropy, we can generate exactly a random variate using only a finite expected number of perfect coin flips. A perfect coin flip is the outcome of an unbiased Bernoulli random…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
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…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…
Generating random bits from a source of biased coins (the biased is unknown) is a classical question that was originally studied by von Neumann. There are a number of known algorithms that have asymptotically optimal information efficiency,…
We present efficient algorithms to generate a bit string in which each bit is set with arbitrary probability. By adopting a hybrid algorithm, i.e., a finite-bit density approximation with correction techniques, we achieve 3.8 times faster…
We study the problem of generating a random variate $X$ from a finite discrete probability distribution $P$ using an entropy source of independent fair coin flips. A classic result from Knuth and Yao shows that the optimal expected number…
We introduce a method for non-uniform random number generation based on sampling a physical process in a controlled environment. We demonstrate one proof-of-concept implementation of the method that reduces the error of Monte Carlo…
In this paper, we present a universal scheme for transforming an arbitrary algorithm for biased 2-face coins to generate random bits from the general source of an m-sided die, hence enabling the application of existing algorithms to general…
This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
In 1976, Knuth and Yao presented an algorithm for sampling from a finite distribution using flips of a fair coin that on average used the optimal number of flips. Here we show how to easily run their algorithm for the special case of…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that $\Delta^4=O(m)$, where $\Delta$ is the maximal degree and $m$ is the number of edges,the algorithm runs in expected…
Non-deterministic random bits are needed in many scientific fields. Unfortunately today's computers are very limited in ability to produce them. We present here a method for extraction of non-deterministic random bits from random physics…