Quantifying Homology Classes II: Localization and Stability

Details Quantifying Homology Classes II: Localization and Stability Quantifying Homology Classes II: Localization and Stability

2007-09-16

arxiv.org/abs/0709.2512v2

Computer Science

Computational Geometry

The "companion paper" referred in this paper is another version of the paper "Measuring and localizing homology classes" by th

Scientific paper

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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