$\newcommand{\Re}{\mathbb{R}}$We study the minWSPD problem of computing the minimum-size well-separated pairs decomposition of a set of points, and show constant approximation algorithms in low-dimensional Euclidean space and doubling metrics. This problem is computationally hard already $\Re^2$, and is also hard to approximate. We also introduce a new pair decomposition, removing the requirement that the diameters of the parts should be small. Surprisingly, we show that in a general metric space, one can compute such a decomposition of size $O( \tfrac{n}{\varepsilon}\log n)$, which is dramatically smaller than the quadratic bound for WSPDs. In $\Re^d$, the bound improves to $O( d \tfrac{n}{\varepsilon}\log \tfrac{1}{\varepsilon } )$.

翻译：$\newcommand{\Re}{\mathbb{R}}$我们研究了计算点集最小规模良分离对分解（minWSPD）的问题，并在低维欧几里得空间和加倍度量空间中提出了常数近似算法。该问题即使在$\Re^2$中已是计算困难的，且难以近似。我们还引入了一种新的对分解方法，取消了各部分直径必须较小的要求。令人惊讶的是，我们证明在一般度量空间中，可以计算出规模为$O( \tfrac{n}{\varepsilon}\log n)$的此类分解，这显著小于WSPD的二次界。在$\Re^d$中，该界改进为$O( d \tfrac{n}{\varepsilon}\log \tfrac{1}{\varepsilon } )$。