An improved algorithm for Generalized \v{C}ech complex construction
Computational Geometry
2022-10-03 v1
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 -simplex, we leverage the computation performed in the round of -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 -simplex can be constructed on the basis of the -simplices. We demonstrate the performance with a comparison to some closely related algorithms.
Keywords
Cite
@article{arxiv.2209.15574,
title = {An improved algorithm for Generalized \v{C}ech complex construction},
author = {Jie Chu and Mikael Vejdemo-Johansson and Ping Ji},
journal= {arXiv preprint arXiv:2209.15574},
year = {2022}
}