Well-separated pair decomposition

In computational geometry, a well-separated pair decomposition (WSPD) of a set of points ${\displaystyle S\subset \mathbb {R} ^{d}}$, is a sequence of pairs of sets ${\displaystyle (A_{i},B_{i})}$, such that each pair is well-separated, and for each two distinct points ${\displaystyle p,q\in S}$, there exists precisely one pair which separates the two.

The graph induced by a well-separated pair decomposition can serve as a k-spanner of the complete Euclidean graph, and is useful in approximating solutions to several problems pertaining to this.