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Maximum Clique Problem
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what information about the cliques, should be found. Common formulations of the clique problem include finding a maximum clique (a clique with the largest possible number of vertices), finding a maximum weight clique in a weighted graph, listing all maximal cliques (cliques that cannot be enlarged), and solving the decision problem of testing whether a graph contains a clique larger than a given size. The clique problem arises in the following real-world setting. Consider a social network, where the graph's vertices represent people, and the graph's edges represent mutual acquaintance. Then a clique represents a subset of people who all know each other, and algorithms for finding cliques can be used to discover these groups of m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brute Force Clique Algorithm
Brute or The Brute may refer to: People * Brute, a pseudonym of English commercial artist Aidan Hughes (born 1956) * "Brute", nickname of US Marine Corps Lieutenant General Victor H. Krulak (1913–2008) * Brute Bernard, ring name of Canadian wrestler Jim Bernard (1921–1984) * Simon Bruté (1779–1839), missionary and first bishop of the Diocese of Vincennes, Indiana * Brutus, the cognomen of an Ancient Roman family whose vocative form is "Brute" * Bill "The Brute" Sanger, a member of the Cherry Hill Gang, a late nineteenth century New York City street gang * The Brute (wrestler), ring name of professional wrestler John Czawlytko in the early 1990s * "The Brute", nickname of American jazz tenor saxophonist Ben Webster (1909–1973) * Marcus Junius Brutus the Younger, a Roman politician and one of Julius Caesar's assassins Arts, entertainment, and media * ''BRUTE!'', a magazine published by English artist Aidan Hughes who also occasionally uses "Brute" as pseudonym * '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameterized Complexity
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to ''multiple'' parameters of the input or output. The complexity of a problem is then measured as a function of those parameters. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number of bits in the input. The first systematic work on parameterized complexity was done by . Under the assumption that P ≠ NP, there exist many natural problems that require superpolynomial running time when complexity is measured in terms of the input size only, but that are computable in a time that is polynomial in the input size and exponential or worse in a parameter . Hence, if is fixed at a small value and the growth of the function over is relatively small then such p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a Chemical reaction, reaction with other Chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time. The field of approximation algorithms, therefore, tries to understand how closely it is possible to approximate optimal solutions to such problems in polynomial time. In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution. However, there are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P ≠ NP
The P versus NP problem is a major unsolved problem in theoretical computer science. In informal terms, it asks whether every problem whose solution can be quickly verified can also be quickly solved. The informal term ''quickly'', used above, means the existence of an algorithm solving the task that runs in polynomial time, such that the time to complete the task varies as a polynomial function on the size of the input to the algorithm (as opposed to, say, exponential time). The general class of questions for which some algorithm can provide an answer in polynomial time is " P" or "class P". For some questions, there is no known way to find an answer quickly, but if one is provided with information showing what the answer is, it is possible to verify the answer quickly. The class of questions for which an answer can be ''verified'' in polynomial time is NP, which stands for "nondeterministic polynomial time".A nondeterministic Turing machine can move to a state that is not d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New York Times
''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid digital subscribers. It also is a producer of popular podcasts such as '' The Daily''. Founded in 1851 by Henry Jarvis Raymond and George Jones, it was initially published by Raymond, Jones & Company. The ''Times'' has won 132 Pulitzer Prizes, the most of any newspaper, and has long been regarded as a national " newspaper of record". For print it is ranked 18th in the world by circulation and 3rd in the U.S. The paper is owned by the New York Times Company, which is publicly traded. It has been governed by the Sulzberger family since 1896, through a dual-class share structure after its shares became publicly traded. A. G. Sulzberger, the paper's publisher and the company's chairman, is the fifth generation of the family to head the pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worst-case Analysis
The worst-case analysis regulation40 CFR 1502.22 was promulgated in 1979 by the US Council on Environmental Quality (CEQ). The regulation is one of many implementing the National Environmental Policy Act of 1969 and it sets out the formal procedure a US government agency must follow when confronted with gaps in relevant information or scientific uncertainty about significant adverse effects on the environment from a major federal action Major (commandant in certain jurisdictions) is a military rank of commissioned officer status, with corresponding ranks existing in many military forces throughout the world. When used unhyphenated and in conjunction with no other indicator .... Synopsis The regulation requires an agency to make known when it is confronted with gaps in relevant information or scientific uncertainty. The agency then must determine if the missing information is essential to a reasoned choice among the alternatives. When the missing information is material to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique
A clique ( AusE, CanE, or ), in the social sciences, is a group of individuals who interact with one another and share similar interests. Interacting with cliques is part of normative social development regardless of gender, ethnicity, or popularity. Although cliques are most commonly studied during adolescence and middle childhood development, they exist in all age groups. They are often bound together by shared social characteristics such as ethnicity and socioeconomic status. Examples of common or stereotypical adolescent cliques include athletes, nerds, and "outsiders". Typically, people in a clique will not have a completely open friend group and can, therefore, "ban" members if they do something considered unacceptable, such as talking to someone disliked. Some cliques tend to isolate themselves as a group and view themselves as superior to others, which can be demonstrated through bullying and other antisocial behaviors. Terminology Within the concepts of sociology, cliqu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey Theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a question of the form: "how big must some structure be to guarantee that a particular property holds?" More specifically, Ron Graham described Ramsey theory as a "branch of combinatorics". Examples A typical result in Ramsey theory starts with some mathematical structure that is then cut into pieces. How big must the original structure be in order to ensure that at least one of the pieces has a given interesting property? This idea can be defined as partition regularity. For example, consider a complete graph of order ''n''; that is, there are ''n'' vertices and each vertex is connected to every other vertex by an edge. A complete graph of order 3 is called a triangle. Now colour each edge either red or blue. How large must ''n'' be in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bron–Kerbosch Algorithm
In computer science, the Bron–Kerbosch algorithm is an enumeration algorithm for finding all maximal cliques in an undirected graph. That is, it lists all subsets of vertices with the two properties that each pair of vertices in one of the listed subsets is connected by an edge, and no listed subset can have any additional vertices added to it while preserving its complete connectivity. The Bron–Kerbosch algorithm was designed by Dutch scientists Coenraad Bron and Joep Kerbosch, who published its description in 1973. Although other algorithms for solving the clique problem have running times that are, in theory, better on inputs that have few maximal independent sets, the Bron–Kerbosch algorithm and subsequent improvements to it are frequently reported as being more efficient in practice than the alternatives. It is well-known and widely used in application areas of graph algorithms such as computational chemistry. A contemporaneous algorithm of , although presented in diff ... [...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] |
Polynomial Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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