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arXiv · 1912.05826

Efficient Approximation of the Matching Distance for 2-parameter persistence

Michael Kerber·Arnur Nigmetov
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Abstract

The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired precision $\epsilon>0$. Our approach is based on a quad-tree refinement strategy introduced by Biasotti et al., but we recast their approach entirely in geometric terms. This point of view leads to several novel observations resulting in a practically faster algorithm. We demonstrate this speed-up by experimental comparison and provide our code in a public repository which provides the first efficient publicly available implementation of the matching distance.

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Michael Kerber, Arnur Nigmetov. 2019-12-12. Efficient Approximation of the Matching Distance for 2-parameter persistence. https://arxiv.org/abs/1912.05826

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