A sparse graph that preserves an approximation of the shortest paths between all pairs of points in a plane is called a geometric spanner. Using range trees of sublinear size, we design an algorithm in massively parallel computation (MPC) model for constructing a geometric spanner known as Yao-graph. This improves the total time and the total memory of existing algorithms for geometric spanners from subquadratic to near-linear.

翻译：能够保持平面中点对间最短路径近似性的稀疏图称为几何伸缩因子图。利用亚线性大小的范围树，我们在大规模并行计算（MPC）模型下设计了一种构建几何伸缩因子图（即Yao图）的算法。该算法将现有几何伸缩因子图算法的总时间与总内存消耗从次平方级优化至近线性级。