Next Article in Journal
Optimal Prefix Free Codes with Partial Sorting
Next Article in Special Issue
Computing Persistent Homology of Directed Flag Complexes
Previous Article in Journal
Comparative Analysis of Different Model-Based Controllers Using Active Vehicle Suspension System
Open AccessArticle

A Numerical Approach for the Filtered Generalized Čech Complex

Departamento de Matemáticas, Universidad de Sonora, C.P. 83000, Hermosillo, Mexico
*
Author to whom correspondence should be addressed.
Algorithms 2020, 13(1), 11; https://doi.org/10.3390/a13010011
Received: 24 November 2019 / Revised: 24 December 2019 / Accepted: 27 December 2019 / Published: 30 December 2019
(This article belongs to the Special Issue Topological Data Analysis)
In this paper, we present an algorithm to compute the filtered generalized Čech complex for a finite collection of disks in the plane, which do not necessarily have the same radius. The key step behind the algorithm is to calculate the minimum scale factor needed to ensure rescaled disks have a nonempty intersection, through a numerical approach, whose convergence is guaranteed by a generalization of the well-known Vietoris–Rips Lemma, which we also prove in an alternative way, using elementary geometric arguments. We give an algorithm for computing the 2-dimensional filtered generalized Čech complex of a finite collection of d-dimensional disks in R d , and we show the performance of our algorithm. View Full-Text
Keywords: disk system; generalized Čech complex; Čech scale; generalized Vietoris–Rips Lemma; miniball problem disk system; generalized Čech complex; Čech scale; generalized Vietoris–Rips Lemma; miniball problem
Show Figures

Graphical abstract

MDPI and ACS Style

Espinoza, J.F.; Hernández-Amador, R.; Hernández-Hernández, H.A.; Ramonetti-Valencia, B. A Numerical Approach for the Filtered Generalized Čech Complex. Algorithms 2020, 13, 11.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop