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Any randomized algorithm may be interpreted as a randomized choice among deterministic algorithms, and thus as a mixed strategy for Alice. Similarly, a non-random algorithm may be thought of as a pure strategy for Alice. In any two-player zero-sum game, if one player chooses a mixed strategy, then the other player has an optimal pure strategy ...
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 ...
Seidel (1991) gave an algorithm for low-dimensional linear programming that may be adapted to the LP-type problem framework. Seidel's algorithm takes as input the set S and a separate set X (initially empty) of elements known to belong to the optimal basis. It then considers the remaining elements one-by-one in a random order, performing ...
swarm algorithms; evolutionary algorithms. genetic algorithms by Holland (1975) [19] evolution strategies; cascade object optimization & modification algorithm (2016) [20] In contrast, some authors have argued that randomization can only improve a deterministic algorithm if the deterministic algorithm was poorly designed in the first place. [21]
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).
In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are the Karger–Stein algorithm [ 1 ] and the Monte Carlo algorithm for minimum feedback arc set .
This follows from submodularity: the marginal utility of g, when added to the remaining bundle, cannot be higher than its marginal utility when the algorithm processed it. So, for every contribution of v to the algorithm welfare, the potential contribution to the optimal welfare could be at most 2v. Therefore, the optimal welfare is at most 2 ...
For example, consider a certain probabilistic algorithm on a graph with n nodes. If the probability that the algorithm returns the correct answer is /, then when the number of nodes is very large, the algorithm is correct with a probability that is very near 1. This fact is expressed shortly by saying that the algorithm is correct WHP.