English

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 kk-simplex, we leverage the computation performed in the round of (k1)(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 kk-simplex can be constructed on the basis of the (k1)(k-1)-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}
}