Algorithmic Version For Szemerédi Regularity Partition
Algorithmic may refer to: *Algorithm, step-by-step instructions for a calculation **Algorithmic art, art made by an algorithm **Algorithmic composition, music made by an algorithm **Algorithmic trading, trading decisions made by an algorithm **Algorithmic patent, an intellectual property right in an algorithm *Algorithmics, the science of algorithms **''Algorithmica'', an academic journal for algorithm research **Algorithmic efficiency, the computational resources used by an algorithm **Algorithmic information theory, study of relationships between computation and information **Algorithmic mechanism design, the design of economic systems from an algorithmic point of view **Algorithmic number theory, algorithms for number-theoretic computation **Algorithmic game theory, game-theoretic techniques for algorithm design and analysis * Algorithmic cooling, a phenomenon in quantum computation *Algorithmic probability In algorithmic information theory, algorithmic probability, also known as ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Art
Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called ''algorists''. Overview Algorithmic art, also known as computer-generated art, is a subset of generative art (generated by an autonomous system) and is related to systems art (influenced by systems theory). Fractal art is an example of algorithmic art. For an image of reasonable size, even the simplest algorithms require too much calculation for manual execution to be practical, and they are thus executed on either a single computer or on a cluster of computers. The final output is typically displayed on a computer monitor, printed with a raster-type printer, or drawn using a plotter. Variability can be introduced by using pseudo-random numbers. There is no consensus as to whether the product of an algorithm that operates on an existing image (or on any input other than pseudo-random numbers) can still be considered comput ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Composition
Algorithmic composition is the technique of using algorithms to create music. 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. The term can be used to describe music-generating techniques that run without ongoing human intervention, for example through the introduction of chance procedures. However through live coding and other interactive interfaces, a fully human-centric approach to algorithmic composition is possible. Some algorithms or data that have no immediate musical relevance are used by composers as creative inspiration for their music. Algorithms such as fractals, L-systems, statistical models, and even arbitrary data (e.g. census figures, GIS coordinates, or magnetic field measurements) have been used as source materials. Models for algorithmic composition Compositional algorithms are u ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Trading
Algorithmic trading is a method of executing orders using automated pre-programmed trading instructions accounting for variables such as time, price, and volume. This type of trading attempts to leverage the speed and computational resources of computers relative to human traders. In the twenty-first century, algorithmic trading has been gaining traction with both retail and institutional traders. It is widely used by investment banks, pension funds, mutual funds, and hedge funds that may need to spread out the execution of a larger order or perform trades too fast for human traders to react to. A study in 2019 showed that around 92% of trading in the Forex market was performed by trading algorithms rather than humans. The term algorithmic trading is often used synonymously with automated trading system. These encompass a variety of trading strategies, some of which are based on formulas and results from mathematical finance, and often rely on specialized software. Examples o ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Patent
A software patent is a patent on a piece of software, such as a computer program, libraries, user interface, or algorithm. Background A patent is a set of exclusionary rights granted by a state to a patent holder for a limited period of time, usually 20 years. These rights are granted to patent applicants in exchange for their disclosure of the inventions. Once a patent is granted in a given country, no person may make, use, sell or import/export the claimed invention in that country without the permission of the patent holder. Permission, where granted, is typically in the form of a license which conditions are set by the patent owner: it may be free or in return for a royalty payment or lump sum fee. Patents are territorial in nature. To obtain a patent, inventors must file patent applications in each and every country in which they want a patent. For example, separate applications must be filed in Japan, China, the United States and India if the applicant wishes to obtain ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmics
Algorithmics is the systematic study of the design and analysis of algorithms. It is fundamental and one of the oldest fields of computer science. It includes algorithm design, the art of building a procedure which can solve efficiently a specific problem or a class of problem, algorithmic complexity theory, the study of estimating the hardness of problems by studying the properties of the algorithm that solves them, or algorithm analysis, the science of studying the properties of a problem, such as quantifying resources in time and memory space needed by this algorithm to solve this problem. The term algorithmics is rarely used in the English-speaking world, where it is synonymous with ''algorithms and data structures''. The term gained wider popularity after the publication of the book ''Algorithmics: The Spirit of Computing'' by David Harel. See also * Divide-and-conquer algorithm * Heuristic * Akra–Bazzi method In computer science, the Akra–Bazzi method, or Akra–Bazzi ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmica
''Algorithmica'' received the highest possible ranking “A*”. External links Springer information Computer science journals Springer Science+Business Media academic journals Monthly journals Publications established in 1986 English-language journals ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Efficiency
In computer science, algorithmic efficiency is a property of an algorithm which relates to the amount of computational resources used by the algorithm. An algorithm must be analyzed to determine its resource usage, and the efficiency of an algorithm can be measured based on the usage of different resources. Algorithmic efficiency can be thought of as analogous to engineering productivity for a repeating or continuous process. For maximum efficiency it is desirable to minimize resource usage. However, different resources such as time and space complexity cannot be compared directly, so which of two algorithms is considered to be more efficient often depends on which measure of efficiency is considered most important. For example, bubble sort and timsort are both algorithms to sort a list of items from smallest to largest. Bubble sort sorts the list in time proportional to the number of elements squared (O(n^2), see Big O notation), but only requires a small amount of extra mem ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Information Theory
Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects (as opposed to stochastically generated), such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" (except for a constant that only depends on the chosen universal programming language) the relations or inequalities found in information theory. According to Gregory Chaitin, it is "the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously." Besides the formalization of a universal measure for irreducible information content of computably generated objects, some main achievements of AIT were to show that: in fact algorithmic complexity follows (in the self-delimited case) the same inequalities (except for a constant) tha ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Mechanism Design
Algorithmic mechanism design (AMD) lies at the intersection of economic game theory, optimization, and computer science. The prototypical problem in mechanism design is to design a system for multiple self-interested participants, such that the participants' self-interested actions at equilibrium lead to good system performance. Typical objectives studied include revenue maximization and social welfare maximization. Algorithmic mechanism design differs from classical economic mechanism design in several respects. It typically employs the analytic tools of theoretical computer science, such as worst case analysis and approximation ratios, in contrast to classical mechanism design in economics which often makes distributional assumptions about the agents. It also considers computational constraints to be of central importance: mechanisms that cannot be efficiently implemented in polynomial time are not considered to be viable solutions to a mechanism design problem. This often, for exam ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Number Theory
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program. Software packages * Magma computer algebra system * SageMath * Number Theory Library * PARI/GP * Fast Library for Number Theory Further reading * * * * * * * * * * * References ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Algorithmic Game Theory
Algorithmic game theory (AGT) is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments. Typically, in Algorithmic Game Theory problems, the input to a given algorithm is distributed among many players who have a personal interest in the output. In those situations, the agents might not report the input truthfully because of their own personal interests. We can see Algorithmic Game Theory from two perspectives: * ''Analysis'': given the currently implemented algorithms, analyze them using Game Theory tools (e.g., calculate and prove properties on their Nash equilibria, price of anarchy, and best-response dynamics) * ''Design'': design games that have both good game-theoretical and algorithmic properties. This area is called algorithmic mechanism design. On top of the usual requirements in classical algorithm design (e.g., ''polynomial-time running time'', ''good approximation ratio), ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |