哪些点的距离是由它们的两两距离的分布决定的？
Which Point Configurations are Determined by the Distribution of their Pairwise Distances?
摘要：
在以前的论文中，我们表明，对于任何$n \ge m+2$，大多数集的$n$点在$\RR^m$确定（旋转，反射，平移和重新标记的点）由其成对距离的分布。但也有一些例外的点的配置，不能重建从上述意义上的距离分布。在本文中，我们提出了一个可重构性测试与运行时间$O(n^{11})$。还讨论了方向保持刚性运动（旋转和平移）和缩放的情况。
英文摘要：
In a previous paper we showed that, for any $n \ge m+2$, most sets of $n$ points in $\RR^m$ are determined (up to rotations, reflections, translations and relabeling of the points) by the distribution of their pairwise distances. But there are some exceptional point configurations which are not reconstructible from the distribution of distances in the above sense. In this paper, we present a reconstructibility test with running time $O(n^{11})$. The cases of orientation preserving rigid motions (rotations and translations) and scalings are also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
