ikkeoverlappende

Ikkeoverlappende, in English non-overlapping, describes objects, regions, or sets that do not share any common part. The term is used across mathematics, computer science, and everyday descriptions of space or time. When items are ikkeoverlappende, their intersection is empty, meaning no element belongs to more than one item.

Formal definition: In a universe X, a family of sets {A_i} is ikkeoverlappende (pairwise disjoint) if for every i ≠ j, the intersection A_i ∩ A_j is empty. This concept extends to intervals, tiles, memory blocks, and time slots. In interval notation, non-overlapping intervals satisfy A_i ∩ A_j = ∅ for i ≠ j, with endpoint conventions affecting whether adjacent intervals are considered overlapping (for example, using half-open intervals [a, b) avoids overlap at a boundary, whereas closed intervals [a, b] may share endpoints).

Examples: Two appointments from 09:00–10:00 and 10:00–11:00 are ikkeoverlappende in a schedule that treats adjacent slots as distinct. In geometry, non-overlapping tiles cover a region without any overlap. In data structures, non-overlapping memory blocks are allocated so that no two blocks share storage.

Applications: The concept is central to scheduling, tiling, and partitioning problems; it underpins algorithms for interval scheduling, graph coloring of interval graphs, and the construction of disjoint sets or partitions. It also informs database range partitioning and file system block allocation, where non-overlap ensures correctness and avoids conflicts.

See also: disjoint sets, non-overlapping intervals, partitioning, tiling, interval scheduling.