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Anytime Algorithm
In computer science, an anytime algorithm is an algorithm that can return a valid solution to a problem even if it is interrupted before it ends. The algorithm is expected to find better and better solutions the longer it keeps running. Most algorithms run to completion: they provide a single answer after performing some fixed amount of computation. In some cases, however, the user may wish to terminate the algorithm prior to completion. The amount of computation required may be substantial, for example, and computational resources might need to be reallocated. Most algorithms either run to completion or they provide no useful solution information. Anytime algorithms, however, are able to return a partial answer, whose quality depends on the amount of computation they were able to perform. The answer generated by anytime algorithms is an approximation of the correct answer. Names An anytime algorithm may be also called an "interruptible algorithm". They are different from contract ...
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Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ...
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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 ...
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Computational Problem
In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring :"Given a positive integer ''n'', find a nontrivial prime factor of ''n''." is a computational problem. A computational problem can be viewed as a set of ''instances'' or ''cases'' together with a, possibly empty, set of ''solutions'' for every instance/case. For example, in the factoring problem, the instances are the integers ''n'', and solutions are prime numbers ''p'' that are the nontrivial prime factors of ''n''. Computational problems are one of the main objects of study in theoretical computer science. The field of computational complexity theory attempts to determine the amount of resources ( computational complexity) solving a given problem will require and explain why some problems are intractable or undecidable. Computational problems belong to complexity classes that define broadly the resources (e.g. time, space/memory, e ...
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Hybrid Intelligent System
Hybrid intelligent system denotes a software system which employs, in parallel, a combination of methods and techniques from artificial intelligence subfields, such as: * Neuro-symbolic systems * Neuro-fuzzy systems * Hybrid connectionist-symbolic models * Fuzzy expert systems * Connectionist expert systems * Evolutionary neural networks * Genetic fuzzy systems * Rough fuzzy hybridization * Reinforcement learning with fuzzy, neural, or evolutionary methods as well as symbolic reasoning methods. From the cognitive science perspective, every natural intelligent system is hybrid because it performs mental operations on both the symbolic and subsymbolic levels. For the past few years, there has been an increasing discussion of the importance of A.I. Systems Integration. Based on notions that there have already been created simple and specific AI systems (such as systems for computer vision, speech synthesis, etc., or software that employs some of the models mentioned above) and ...
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Artificial Intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech recognition, computer vision, translation between (natural) languages, as well as other mappings of inputs. The ''Oxford English Dictionary'' of Oxford University Press defines artificial intelligence as: the theory and development of computer systems able to perform tasks that normally require human intelligence, such as visual perception, speech recognition, decision-making, and translation between languages. AI applications include advanced web search engines (e.g., Google), recommendation systems (used by YouTube, Amazon and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Tesla), automated decision-making and competing at the highest level in strategic game systems (such as chess and Go). ...
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Newton–Raphson
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function defined for a real variable , the function's derivative , and an initial guess for a root of . If the function satisfies sufficient assumptions and the initial guess is close, then :x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the intersection of the -axis and the tangent of the graph of at : that is, the improved guess is the unique root of the linear approximation at the initial point. The process is repeated as :x_ = x_n - \frac until a sufficiently precise value is reached. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions an ...
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Problem Solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices. Solutions require sufficient resources and knowledge to attain the goal. Professionals such as ...
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Distributed Computing
A distributed system is a system whose components are located on different computer network, networked computers, which communicate and coordinate their actions by message passing, passing messages to one another from any system. Distributed computing is a field of computer science that studies distributed systems. The components of a distributed system interact with one another in order to achieve a common goal. Three significant challenges of distributed systems are: maintaining concurrency of components, overcoming the clock synchronization, lack of a global clock, and managing the independent failure of components. When a component of one system fails, the entire system does not fail. Examples of distributed systems vary from service-oriented architecture, SOA-based systems to massively multiplayer online games to peer-to-peer, peer-to-peer applications. A computer program that runs within a distributed system is called a distributed program, and ''distributed programming' ...
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Dynamic Programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have ''optimal substructure''. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.Cormen, T. H.; Leiserson, C. E.; Rives ...
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Mathematical Statistics
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Introduction Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling. The initial analysis of the data often follows the study protocol specified prior to the study being conducted. The data from a study can also be analyzed to consider secondary hypotheses inspired by the initial results, or to suggest new studies. A secondary analysis of the data from a planned study uses tools from data analysis, and the process of doing this is mathematical statistics. Data analysis is divided into: * descriptive statistics - the part of st ...
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Travelling Salesman Problem
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP. In the theory of computational complexity, the decision version of the TSP (where given a length ''L'', the task is to decide whether the graph has a tour of at most ''L'') belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied p ...
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Bubble Sort
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps had to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list. This simple algorithm performs poorly in real world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java. Analysis Performance Bubble sort has a worst-case and average complexity of O(n^2), where n is the number of items being sorted. Most practical sorting algorithms have substantially better worst-case or average complexity, ...
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