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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 ...
A company is run by the directors, who are appointed by the shareholders. Usually, the shareholders elect a board of directors (BOD) at the annual general meeting (AGM), which may be statutory (e.g. India and the UK). The number of directors depends on the size of the company and statutory requirements.
Here, a Las Vegas algorithm is a randomized algorithm whose runtime may vary, but for which the result is always correct. [ 7 ] [ 8 ] For example, this form of Yao's principle has been used to prove the optimality of certain Monte Carlo tree search algorithms for the exact evaluation of game trees .
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The algorithm will then use ⌈ / ⌉ multiplications, where was the number of half-words in the vector. Thus, the algorithm runs at a "rate" of one multiplication per word of input. The same scheme can also be used for hashing integers, by interpreting their bits as vectors of bytes.
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).
It starts from an assumption about a probabilistic distribution of the set of all possible inputs. This assumption is then used to design an efficient algorithm or to derive the complexity of a known algorithm. This approach is not the same as that of probabilistic algorithms, but the two may be combined.
A Monte Carlo algorithm is a randomized algorithm which is likely to be correct. Problems in the class BPP have Monte Carlo algorithms with polynomial bounded running time. This is compared to a Las Vegas algorithm which is a randomized algorithm which either outputs the correct answer, or outputs "fail" with low probability.