For a set S of points in ℝ(d), an s-spanner is a subgraph of the complete graph with node set S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1 + ε)-spanner with O(n/ε(d)) edges, where ε is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion of points, as well as under continuous motion of the points in both the kinetic data structures setting and in the more realistic blackbox displacement model we introduce. Our deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), well-separated pair decompositions, and approximate k-centers.

中文翻译：

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可变形扳手和应用。

对于 ℝ(d) 中的点集合 S，s-spanner 是具有节点集 S 的完整图的子图，使得任何一对点都通过 spanner 中的某个路径连接，其总长度至多是点之间的欧几里得距离。在本文中，我们提出了一种新的具有 O(n/ε(d)) 边的稀疏 (1 + ε)-spanner，其中 ε 是指定参数。这个扳手的关键特性是它可以在点的动态插入或删除下，以及在动力学数据结构设置和我们引入的更真实的黑盒位移模型中点的连续运动下有效地维护。我们的可变形扳手简洁地编码了变形点云中的所有邻近信息，为我们提供了有效的动力学算法来解决诸如最近对、所有点的近邻、