Paralleliset

Paralleliset is a term used across different disciplines to denote a construction that involves parallelism or parallel copies of a base object. In geometry, the parallel set of a subset A of Euclidean space with radius r is the set of all points whose distance to A is at most r. This r-parallel set, also called the offset of A, is a standard object in geometric measure theory and is used in image processing, computer graphics, and the study of curvature and surface area. Its boundary, the offset boundary, provides a way to approximate and quantify the shape of A at a fixed distance.

In computing and data processing, paralleliset is sometimes used informally to describe a collection of sets that can be processed in parallel or a theoretical data structure that supports parallel operations on multiple sets, such as parallel union, intersection, or difference. The term is not widely standardized and appears primarily in project documentation or speculative discussions about parallel set processing.

In the field of corpus linguistics and natural language processing, paralleliset can refer to a corpus of parallel texts—translations of the same material into multiple languages—used for alignment, bilingual lexicon induction, and evaluation of machine translation systems.

Etymology and usage: Paralleliset combines parallel and set. The precise meaning varies by discipline, and it is generally better defined within a given context rather than as a single universal concept.

See also: parallel set (geometry), Minkowski sum, offset, parallel processing, set theory, corpus linguistics.