Let $t>1$ be a real number. A geometric t-spanner is a geometric graph for a point set in ${\mathbb{R}}^d$ with straight line segments between vertices such that the ratio of the shortest-path distance between every pair of vertices in the graph (with Euclidean edge lengths) to their actual Euclidean distance is at most t.

An imprecise point set is modeled by a set R of regions in ${\mathbb{R}}^d$. If one chooses a point inside each region of R, then the resulting point set is called a precise instance from R. An imprecise t-spanner for an imprecise point set R is a graph $G=(R,E)$ such that for each precise instance S from R, graph $G_S=(S,E_S)$, where $E_S$ is the set of edges corresponding to E and S, is a t-spanner.

In this paper, we show an imprecise point set R of n straight-line segments in the plane such that any imprecise t-spanner for R has $\mathrm{\Omega }(n^2)$ edges. Then, we give an algorithm that computes an imprecise t-spanner for a set of n pairwise disjoint d-dimensional balls with arbitrary sizes. This imprecise t-spanner has $\mathcal{O}(n/{(t-1)}^d)$ edges and can be computed in $\mathcal{O}(n\log n/{(t-1)}^d)$ time. Finally, we show that given an imprecise spanner, finding a precise instance such that its corresponding precise spanner has minimum dilation between all possible precise instances of the imprecise spanner is NP-hard, no matter if crossing edges are allowed or not.

让$t>1$是一个实数。几何t形扳手是一个点集的几何图形${\mathbb{右}}^d$顶点之间有直线段，使得图中每对顶点之间的最短路径距离（具有欧几里德边长度）与其实际欧几里德距离的比率至多为t。

不精确的点集由区域集R建模${\mathbb{右}}^d$。如果选择R的每个区域内的一个点，则生成的点集称为R的精确实例。不精确点集R的不精确t扳手是一个图$G=（右,乙）$这样对于R中的每个精确实例S，图$G_S=（S,{乙}_S）$， 在哪里${乙}_S$是对应于E和S的边集，是一个t扳手。

在本文中，我们展示了平面中n条直线段的不精确点集R ，使得R的任何不精确t跨度都有$\mathrm{\Omega }（n^2）$边缘。然后，我们给出一种算法，为一组n 个任意大小的两两不相交的d维球计算不精确的t跨度。这种不精确的T形扳手有$\mathcal{氧}（n/{（t-1）}^d）$边并且可以计算为$\mathcal{氧}（n\mathrm{日志}n/{（t-1）}^d）$时间。最后，我们表明，给定一个不精确扳手，找到一个精确实例，使其相应的精确扳手在不精确扳手的所有可能精确实例之间具有最小膨胀是 NP 困难的，无论是否允许交叉边缘。