Nonlinear programmingIn mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
Linear programming relaxationIn mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.
Complex instruction set computerA complex instruction set computer (CISC ˈsɪsk) is a computer architecture in which single instructions can execute several low-level operations (such as a load from memory, an arithmetic operation, and a memory store) or are capable of multi-step operations or addressing modes within single instructions. The term was retroactively coined in contrast to reduced instruction set computer (RISC) and has therefore become something of an umbrella term for everything that is not RISC, where the typical differentiating characteristic is that most RISC designs use uniform instruction length for almost all instructions, and employ strictly separate load and store instructions.
Ramsey's theoremIn combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (say, blue and red), let r and s be any two positive integers. Ramsey's theorem states that there exists a least positive integer R(r, s) for which every blue-red edge colouring of the complete graph on R(r, s) vertices contains a blue clique on r vertices or a red clique on s vertices.
Hereditary propertyIn mathematics, a hereditary property is a property of an object that is inherited by all of its subobjects, where the meaning of subobject depends on the context. These properties are particularly considered in topology and graph theory, but also in set theory. In topology, a topological property is said to be hereditary if whenever a topological space has that property, then so does every subspace of it. If the latter is true only for closed subspaces, then the property is called weakly hereditary or closed-hereditary.
Instruction set architectureIn computer science, an instruction set architecture (ISA), also called computer architecture, is an abstract model of a computer. A device that executes instructions described by that ISA, such as a central processing unit (CPU), is called an implementation. In general, an ISA defines the supported instructions, data types, registers, the hardware support for managing main memory, fundamental features (such as the memory consistency, addressing modes, virtual memory), and the input/output model of a family of implementations of the ISA.
Kempe chainIn mathematics, a Kempe chain is a device used mainly in the study of the four colour theorem. Intuitively, it is a connected chain of points on a graph with alternating colors. Kempe chains were first used by Alfred Kempe in his attempted proof of the four colour theorem. Even though his proof turned out to be incomplete, the method of Kempe chains is crucial to the successful modern proofs (Appel & Haken, Robertson et al., etc.). Furthermore, the method is used in the proof of the five-colour theorem by Percy John Heawood, a weaker form of the four-colour theorem.
Cell (processor)Cell is a 64-bit multi-core microprocessor microarchitecture that combines a general-purpose PowerPC core of modest performance with streamlined coprocessing elements which greatly accelerate multimedia and vector processing applications, as well as many other forms of dedicated computation. It was developed by Sony, Toshiba, and IBM, an alliance known as "STI". The architectural design and first implementation were carried out at the STI Design Center in Austin, Texas over a four-year period beginning March 2001 on a budget reported by Sony as approaching US$400 million.
Manycore processorManycore processors are special kinds of multi-core processors designed for a high degree of parallel processing, containing numerous simpler, independent processor cores (from a few tens of cores to thousands or more). Manycore processors are used extensively in embedded computers and high-performance computing. Manycore processors are distinct from multi-core processors in being optimized from the outset for a higher degree of explicit parallelism, and for higher throughput (or lower power consumption) at the expense of latency and lower single-thread performance.
Assignment problemThe assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform as many tasks as possible by assigning at most one agent to each task and at most one task to each agent, in such a way that the total cost of the assignment is minimized.
