Oxford English DictionaryThe Oxford English Dictionary (OED) is the principal historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a comprehensive resource to scholars and academic researchers, as well as describing usage in its many variations throughout the world. Work began on the dictionary in 1857, but it was only in 1884 that it began to be published in unbound fascicles as work continued on the project, under the name of A New English Dictionary on Historical Principles; Founded Mainly on the Materials Collected by The Philological Society.
Computational resourceIn computational complexity theory, a computational resource is a resource used by some computational models in the solution of computational problems. The simplest computational resources are computation time, the number of steps necessary to solve a problem, and memory space, the amount of storage needed while solving the problem, but many more complicated resources have been defined. A computational problem is generally defined in terms of its action on any valid input.
Chinese dictionaryChinese dictionaries date back over two millennia to the Han dynasty, which is a significantly longer lexicographical history than any other language. There are hundreds of dictionaries for the Chinese language, and this article discusses some of the most important. The general term císhū (辭書, "lexicographic books") semantically encompasses "dictionary; lexicon; encyclopedia; glossary". The Chinese language has two words for dictionary: zidian (character/logograph dictionary) for written forms, that is, Chinese characters, and cidian (word/phrase dictionary), for spoken forms.
PiecewiseIn mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself. A distinct, but related notion is that of a property holding piecewise for a function, used when the domain can be divided into intervals on which the property holds.
Time complexityIn 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.
Approximation algorithmIn 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.
Approximations of πApproximations for the mathematical constant pi (pi) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era. In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century. Further progress was not made until the 15th century (through the efforts of Jamshīd al-Kāshī).
Knapsack problemThe knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
Hardness of approximationIn computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Hardness of approximation complements the study of approximation algorithms by proving, for certain problems, a limit on the factors with which their solution can be efficiently approximated. Typically such limits show a factor of approximation beyond which a problem becomes NP-hard, implying that finding a polynomial time approximation for the problem is impossible unless NP=P.
Computational problemIn 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.
Model of computationIn computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology.
