---
res:
bibo_abstract:
- Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r
consists of all points in ℝd that have k or more points of X within distance r.
We consider two filtrations - one in scale obtained by fixing k and increasing
r, and the other in depth obtained by fixing r and decreasing k - and we compute
the persistence diagrams of both. While standard methods suffice for the filtration
in scale, we need novel geometric and topological concepts for the filtration
in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal
integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module
from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.
@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Edelsbrunner, Herbert
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
- foaf_Person:
foaf_givenName: Georg F
foaf_name: Osang, Georg F
foaf_surname: Osang
foaf_workInfoHomepage: http://www.librecat.org/personId=464B40D6-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.4230/LIPIcs.SoCG.2018.34
bibo_volume: 99
dct_date: 2018^xs_gYear
dct_language: eng
dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
dct_title: The multi-cover persistence of Euclidean balls@
...