Randomized Algorithms

An algorithm that makes random (or pseudorandom) choices.

In statistics and statistical physics, the Metropolis-Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult.

In order to warrant the high-probability time bounds, it must randomly permute the input, which changes the relative order of equal elements and shuffles any presorted input.

In this randomized algorithm, α β → 1 {\displaystyle \alpha _{\beta }\rightarrow 1} if β → 1 {\displaystyle \beta \rightarrow 1} .

The Schwartz-Zippel algorithm provides a practical probabilistic solution, by simply randomly testing inputs and checking whether the output is zero.

A Boltzmann sampler is an algorithm intended for random sampling of combinatorial structures.

The Swendsen-Wang algorithm is the first non-local or cluster algorithm for Monte Carlo simulation for large systems near criticality.

The lemma states that evaluating a nonzero polynomial on inputs chosen randomly from a large-enough set is likely to find an input that produces a nonzero output. it was discovered independently by Jack Schwartz, Richard Zippel, and Richard DeMillo and Richard J.

with respect to a randomly drawn belief

Dixon's random squares method

The technique uses the Monte Carlo method to compute estimates of global illumination

we can pick random integers a not divisible by p and see whether the congruence holds

are a broad class of computational algorithms based on repeated random sampling for obtaining numerical results