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arXiv · 2209.15574

An improved algorithm for Generalized \v{C}ech complex construction

Jie Chu·Mikael Vejdemo-Johansson·Ping Ji
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Abstract

In this paper, we present an algorithm that computes the generalized \v{C}ech complex for a finite set of disks where each may have a different radius in 2D space. An extension of this algorithm is also proposed for a set of balls in 3D space with different radius. To compute a $k$-simplex, we leverage the computation performed in the round of $(k-1)$-simplices such that we can reduce the number of potential candidates to verify to improve the efficiency. An efficient verification method is proposed to confirm if a $k$-simplex can be constructed on the basis of the $(k-1)$-simplices. We demonstrate the performance with a comparison to some closely related algorithms.

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Jie Chu, Mikael Vejdemo-Johansson, Ping Ji. 2022-09-30. An improved algorithm for Generalized \v{C}ech complex construction. https://arxiv.org/abs/2209.15574

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