OVERLAP

Overlap is the extent to which two or more objects, sets, intervals, or phenomena share common elements or space. It indicates redundancy, compatibility, or concurrency, and can range from zero (disjoint) to total (one entirely contained within another). The term is context-dependent and quantified by the size of the shared portion relative to the whole.

In geometry, overlap refers to the region that belongs to both objects. For intervals on a line, two intervals [a,b] and [c,d] overlap when max(a,c) < min(b,d); the overlap length is min(b,d) − max(a,c) if positive. In set theory, overlap corresponds to a nonempty intersection A ∩ B ≠ ∅.

In probability and statistics, overlap describes the likelihood of simultaneous occurrences. P(A ∩ B) measures joint occurrence. The overlap coefficient, defined as P(A ∩ B) / min(P(A), P(B)), gauges similarity of two events or distributions, bounded between 0 and 1.

In time-based contexts, overlapping events or tasks run concurrently, which can enable parallel work but may require synchronization or resource management. In data processing, overlapping windows in a rolling analysis trade independence for continuity and smoother estimates.

Overlap is also a descriptive concept in other domains, such as signal processing where windowing uses overlap to avoid artifacts, and in design and collaboration where overlapping responsibilities can cause ambiguity or synergy.