Algorithms for Almost-Uniform Generation with an Unbiased Binary Source
We consider the problem of uniform generation of random integers in the range [1, n] given only a binary source of randomness. Standard models of randomized algorithms (e.g. probabilistic Turing machines) assume the availability of a random binary source that can generate independent random bits in unit time with uniform probability. This makes the task trivial if n is a power of 2. However, exact uniform generation algorithms with bounded run time do not exist if n is not a power of 2.
KeywordsRandom number generation uniform distribution Markov chain rapid mixing eigenvalue circulant matrix
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