Algorithms are essential to the way computers process data.

Algorithms used earlier in the history of cryptography are substantially different from modern methods, and modern ciphers can be classified according to how they operate and whether they use one or two keys.

The results of such Genetic Algorithms are frequently irreducibly complex since the process, like evolution, both removes non-essential components over time as well as adding new components.

Algorithms are generally quite specifically tuned to a particular type of file: for example, lossless audio compression programs do not work well on text files, and vice versa.

Algorithms that are much more efficient than trial division have been devised to test the primality of large numbers.

Algorithms for searching virtual spaces are used in constraint satisfaction problem, where the goal is to find a set of value assignments to certain variables that will satisfy specific mathematical equations and inequations.

Algorithms based on row or column reduction, that is, Gaussian elimination, presented in introductory linear algebra textbooks and in the preceding sections of this article are not suitable for a practical computation of the null space because of numerical accuracy problems in the presence of rounding errors.

Algorithms for vector processors are usually different than those for scalar processors since they can process multiple instructions and / or multiple data elements in parallel ( for examples of these differences see ' description ' in the main article ).

Algorithms designed for this class of processor therefore require more care if they are not to unwittingly disrupt the potential gains.

Algorithms that are asymptotically faster than those of Bareiss and Levinson have been described in the literature.

* Estimation of distribution algorithm, or Probabilistic Model-Building Genetic Algorithms ( PMBGA ), in genetic algorithms, candidate solutions to a problem are represented by a probability distribution

Further references and technical results are discussed in Part II of Geometric Folding Algorithms .< ref name =" GFALOP ">

Algorithms with running time n lb n are sometimes called linearithmic.

# New Media as Faster Execution of Algorithms Previously Executed Manually or through Other Technologies – Computers are a huge speed-up of what were previously manual techniques.

Subjects are Communications, Programming Paradigms, Algorithms, Network Programming, Software Engineering.

Algorithms such as fractals, L-systems, statistical models, and even arbitrary data ( e. g. census figures, GIS coordinates, or magnetic field measurements ) are fair game for musical interpretation.

* Algorithms ( competition length about 2 hours ): Competitors are given a set ( usually three ) of algorithmic problems and have 75 minutes to correctly solve as many as they can.

</ br > Cryptographic Hash Algorithms ( 256-bit or larger digests are to be preferred in new designs.

Algorithms for the conversion of IUPAC names to structure representations and vice versa are also used for extracting structural information from text.

Here are some of most popular variations of ACO Algorithms

Algorithms for ICA include infomax, FastICA, and JADE, but there are many others.

Algorithms for finding strongly connected components may be used to solve 2-satisfiability problems ( systems of Boolean variables with constraints on the values of pairs of variables ): as showed, a 2-satisfiability instance is unsatisfiable if and only if there is a variable v such that v and its complement are both contained in the same strongly connected component of the implication graph of the instance.

Algorithms for computing minimum spanning trees have been intensively studied ; it is known how to solve the problem in linear randomized expected time in a comparison model of computation, or in linear time in a model of computation in which the edge weights are small integers and bitwise operations are allowed on their binary representations.

In computer science, Algorithms for Recovery and Isolation Exploiting Semantics, or ARIES is a recovery algorithm designed to work with a no-force, steal database approach ; it is used by IBM DB2, Microsoft SQL Server and many other database systems.

Algorithms ( or, at the very least, formal sets of rules ) have been used to compose music for centuries ; the procedures used to plot voice-leading in Western counterpoint, for example, can often be reduced to algorithmic determinacy.

It is also used in the Computational Geometry Algorithms Library ( CGAL ) because geometry algorithms tend to ' explode ' when using ordinary floating point CPU math.

KASUMI was designed for 3GPP to be used in UMTS security system by the Security Algorithms Group of Experts

The symmetric encryption algorithm used will vary depending on the version and configuration of the operating system ; see Algorithms used by Windows version below.

Algorithms and mathematical methods used in computational science are varied.

Algorithms for drawing kolams are used in development of Picture drawing Computer software.

Algorithms and techniques used to attain color constancy are frequently used for color balancing, as well.

Algorithms can also be used to route data to data centers where electricity is less expensive.

Algorithms used for the same purpose:

One of these, " Entropy-based Algorithms for Best Basis Selection " led to the WSQ image compression algorithm, used by the FBI to encode fingerprint images.

Algorithms are used in the ground receivers to delete replies on the edge of the two beam patterns.

Algorithms with better asymptotic running time than the Strassen algorithm are rarely used in practice.

Algorithms for calculating variance play a major role in statistical computing.

# Donald E. Knuth, Selected Papers on Analysis of Algorithms ( Stanford, California: Center for the Study of Language and Information — CSLI Lecture Notes, no.

# Donald E. Knuth, Selected Papers on Design of Algorithms ( Stanford, California: Center for the Study of Language and Information — CSLI Lecture Notes, no.

* Paul M. Embree, Damon Danieli: C ++ Algorithms for Digital Signal Processing, Prentice Hall, ISBN 0-13-179144-3

* Richard P. Brent, " Recent Progress and Prospects for Integer Factorisation Algorithms ", Computing and Combinatorics ", 2000, pp. 3-22. download

* Algorithms for the K-server problem

* Algorithms for calculating variance

Algorithms for these problems include the basic brute-force search ( also called " naïve " or " uninformed " search ), and a variety of heuristics that try to exploit partial knowledge about structure of the space, such as linear relaxation, constraint generation, and constraint propagation.

Algorithms have been developed to ensure the same SMILES is generated for a molecule regardless of the order of atoms in the structure.

* Algorithms for calculating variance

* Michel Raynal: Algorithms for Mutual Exclusion, MIT Press, ISBN 0-262-18119-3

* Goldberg, David E ( 2002 ), The Design of Innovation: Lessons from and for Competent Genetic Algorithms, Addison-Wesley, Reading, MA.

* Schmitt, Lothar M ( 2004 ), Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling, Theoretical Computer Science 310: 181 – 231

* James J. Nutaro, Building Software for Simulation: Theory and Algorithms, with Applications in C ++.

Algorithms for cladograms include least squares, neighbor-joining, parsimony, maximum likelihood, and Bayesian inference.

One potential method for determining underpricing is through the use of IPO Underpricing Algorithms.

* Huang, Te-Ming ; Kecman, Vojislav ; and Kopriva, Ivica ( 2006 ); Kernel Based Algorithms for Mining Huge Data Sets, in Supervised, Semi-supervised, and Unsupervised Learning, Springer-Verlag, Berlin, Heidelberg, 260 pp. 96 illus., Hardcover, ISBN 3-540-31681-7

The following EBNF-like grammar ( for Niklaus Wirth's PL / 0 programming language, from Algorithms + Data Structures = Programs ) is in LL ( 1 ) form:

* Algorithms for finding the solution to a NLLSQ problem require initial values for the parameters, LLSQ does not.