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A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are ...
The basic RO algorithm can then be described as: Initialize x with a random position in the search-space. Until a termination criterion is met (e.g. number of iterations performed, or adequate fitness reached), repeat the following: Sample a new position y by adding a normally distributed random vector to the current position x
The following example illustrates how randomized rounding can be used to design an approximation algorithm for the set cover problem. Fix any instance c , S {\displaystyle \langle c,{\mathcal {S}}\rangle } of set cover over a universe U {\displaystyle {\mathcal {U}}} .
The optimal performance that can be obtained by a random algorithm on a deterministic input (its expected complexity), for an algorithm chosen to have the best performance on its worst case inputs, and the worst case input to the algorithm; Yao's principle is often used to prove limitations on the performance of randomized algorithms, by ...
Las Vegas algorithms were introduced by László Babai in 1979, in the context of the graph isomorphism problem, as a dual to Monte Carlo algorithms. [3] Babai [4] introduced the term "Las Vegas algorithm" alongside an example involving coin flips: the algorithm depends on a series of independent coin flips, and there is a small chance of failure (no result).
the proper sampling technique is used; the algorithm used is valid for what is being modeled; it simulates the phenomenon in question. Pseudo-random number sampling algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given probability distribution.
Then, there might be a tie. Following the weight update rule in weighted majority algorithm, the predictions made by the algorithm would be randomized. The algorithm calculates the probabilities of experts predicting positive or negatives, and then makes a random decision based on the computed fraction: [further explanation needed] predict
Reservoir sampling is a family of randomized algorithms for choosing a simple random sample, without replacement, of k items from a population of unknown size n in a single pass over the items. The size of the population n is not known to the algorithm and is typically too large for all n items to fit into main memory. The population is ...