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.
Computational complexityIn computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.
Randomized algorithmA randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables.
Parameterized complexityIn 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.
Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.
Complexity classIn computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.
Space complexityThe space complexity of an algorithm or a computer program is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely. This includes the memory space used by its inputs, called input space, and any other (auxiliary) memory it uses during execution, which is called auxiliary space. Similar to time complexity, space complexity is often expressed asymptotically in big O notation, such as etc.
Reduction (complexity)In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem A is reducible to problem B, if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B.
Algorithmic efficiencyIn 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.
TensorIn mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product.
Contorsion tensorThe contorsion tensor in differential geometry is the difference between a connection with and without torsion in it. It commonly appears in the study of spin connections. Thus, for example, a vielbein together with a spin connection, when subject to the condition of vanishing torsion, gives a description of Einstein gravity. For supersymmetry, the same constraint, of vanishing torsion, gives (the field equations of) 11-dimensional supergravity.
Tensor productIn mathematics, the tensor product of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map that maps a pair to an element of denoted An element of the form is called the tensor product of v and w. An element of is a tensor, and the tensor product of two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span in the sense that every element of is a sum of elementary tensors.
Torsion tensorIn differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet–Serret formulas, for instance, quantifies the twist of a curve about its tangent vector as the curve evolves (or rather the rotation of the Frenet–Serret frame about the tangent vector). In the geometry of surfaces, the geodesic torsion describes how a surface twists about a curve on the surface.
Air conditioningAir conditioning, often abbreviated as A/C (US), AC (US), or air con (UK), is the process of removing heat from an enclosed space to achieve a more comfortable interior environment (sometimes referred to as "comfort cooling") and in some cases also strictly controlling the humidity of internal air. Air conditioning can be achieved using a mechanical air conditioner or alternatively a variety of other methods, including passive cooling or ventilative cooling.
Shor's algorithmShor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.
Continued fractionIn mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression.
Solar air conditioningSolar air conditioning, or "solar-powered air conditioning", refers to any air conditioning (cooling) system that uses solar power. This can be done through passive solar design, solar thermal energy conversion, and photovoltaic conversion (sunlight to electricity). The U.S. Energy Independence and Security Act of 2007 created 2008 through 2012 funding for a new solar air conditioning research and development program, which should develop and demonstrate multiple new technology innovations and mass production economies of scale.
AlgorithmIn mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.
Heating, ventilation, and air conditioningHeating, ventilation, and air conditioning (HVAC) is the use of various technologies to control the temperature, humidity, and purity of the air in an enclosed space. Its goal is to provide thermal comfort and acceptable indoor air quality. HVAC system design is a subdiscipline of mechanical engineering, based on the principles of thermodynamics, fluid mechanics, and heat transfer. "Refrigeration" is sometimes added to the field's abbreviation as HVAC&R or HVACR, or "ventilation" is dropped, as in HACR (as in the designation of HACR-rated circuit breakers).
Outer measureIn the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures.
