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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 ...
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 deterministic algorithm emulates the randomized rounding scheme: it considers each set in turn, and chooses ′ {,}. But instead of making each choice randomly based on x ∗ {\displaystyle x^{*}} , it makes the choice deterministically , so as to keep the conditional probability of failure, given the choices so far, below 1 .
Some problems which do not have a PTAS may admit a randomized algorithm with similar properties, a polynomial-time randomized approximation scheme or PRAS.A PRAS is an algorithm which takes an instance of an optimization or counting problem and a parameter ε > 0 and, in polynomial time, produces a solution that has a high probability of being within a factor ε of optimal.
The model for a randomized block design with one nuisance variable is = + + + where Y ij is any observation for which X 1 = i and X 2 = j X 1 is the primary factor X 2 is the blocking factor μ is the general location parameter (i.e., the mean)
Random sample consensus (RANSAC) is an iterative method to estimate parameters of a mathematical model from a set of observed data that contains outliers, when outliers are to be accorded no influence [clarify] on the values of the estimates. Therefore, it also can be interpreted as an outlier detection method. [1]