Unconstrained and Curvature-Constrained Shortest-Path Distances and Their Approximation
Unconstrained and Curvature-Constrained Shortest-Path Distances and Their Approximation
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无约束和曲率约束的最短路径距离及其近似
DOI：
10.1007/s00454-019-00060-7
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发表时间：
2017
影响因子：
0.8
通讯作者：
Thibaut Le Gouic
中科院分区：
文献类型：
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作者：
E. Arias;Thibaut Le Gouic
我们研究最短路径和它们的距离上的一个子集的欧几里得空间，和他们的近似等价物在一个邻域图上定义的样本从该子集。特别是，我们恢复和推广的结果伯恩斯坦等人。（图近似测地线嵌入流形，技术。代表：斯坦福大学心理学系，2000年）。我们对曲率约束的最短路径和它们的距离做同样的事情，建立我们认为是它们的第一近似界。
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of Bernstein et al. (Graph approximations to geodesics on embedded manifolds, Tech. Rep., Department of Psychology, Stanford University, 2000). We do the same with curvature-constrained shortest paths and their distances, establishing what we believe are the first approximation bounds for them.