量化同源类II：局部化和稳定性
Quantifying Homology Classes II: Localization and Stability
摘要：
在配套文件中，我们测量的同调类和计算的最佳同调基。本文讨论两个相关的问题，即本地化和稳定性。我们局部化一个类的循环最小化某个目标函数。我们探讨了三种不同的目标函数，即体积，直径和半径。我们证明了用前两者计算最小圈是NP-难的。我们还证明了在配套文件中定义的测量是稳定的有关空间的几何形状的小变化。
英文摘要：
In the companion paper, we measured homology classes and computed the optimal homology basis. This paper addresses two related problems, namely, localization and stability. We localize a class with the cycle minimizing a certain objective function. We explore three different objective functions, namely, volume, diameter and radius. We show that it is NP-hard to compute the smallest cycle using the former two. We also prove that the measurement defined in the companion paper is stable with regard to small changes of the geometry of the concerned space.
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