minmid

Minmid is a term encountered in a small subset of mathematical and algorithmic discussions, used to denote the minimum of midpoints within a collection of numbers or points. It is not a standardized concept with a single formal definition across disciplines, but rather a name given to a simple pairwise statistic or heuristic in certain contexts.

In mathematics, the minmid of a finite set of real numbers or points in one or two dimensions can be defined as the minimum value among the midpoints of all unordered pairs drawn from the set. For a set {a, b, c}, the midpoints are (a + b)/2, (a + c)/2, and (b + c)/2, and minmid is the smallest of these three values. In higher dimensions, midpoints are computed componentwise, and the minimum is taken across all pairwise midpoints.

In algorithmic use, minmid can serve as a data reduction or pivot-selection rule. A minmid-based heuristic might choose the pair with the smallest midpoint to anchor a clustering centroid, to define a split point, or to select a representative sample. Its computational cost is typically quadratic in the input size because it involves examining all unordered pairs.

In programming practice, minmid may appear as a function name in lightweight libraries or as pseudocode, defined as the minimum of the set of pairwise midpoints. Because minmid is a coined term with varying usage, the precise interpretation can differ between sources, and readers should consult the surrounding definitions in any given context.