TY - JOUR
T1 - A numerical approach for the filtered generalized Čech complex
AU - Espinoza, Jesús F.
AU - Hernández-Amador, Rosalía
AU - Hernández-Hernández, Héctor A.
AU - Ramonetti-Valencia, Beatriz
N1 - Publisher Copyright:
© 2019 by the authors.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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 Rd, and we show the performance of our algorithm.
AB - 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 Rd, and we show the performance of our algorithm.
KW - Disk system
KW - Generalized vietoris-rips lemma
KW - Generalized Čech complex
KW - Miniball problem
KW - Čech scale
UR - http://www.scopus.com/inward/record.url?scp=85078700176&partnerID=8YFLogxK
U2 - 10.3390/a13010011
DO - 10.3390/a13010011
M3 - Artículo
AN - SCOPUS:85078700176
VL - 13
JO - Algorithms
JF - Algorithms
IS - 1
M1 - 11
ER -