5 papers
Lunar Generalizations of the Euclidean Minimum Spanning Tree in the Plane and their Expected Costs
Ondřej Draganov, Herbert Edelsbrunner, Sophie Rosenmeier +1
Motivated by the recent introduction of chromatic persistent homology, we generalize the Euclidean minimum spanning tree (EMST) for points in to the lunar EMST f…
Expected Length of the Euclidean Minimum Spanning Tree and 1-norms of Chromatic Persistence Diagrams in the Plane
Ondřej Draganov, Herbert Edelsbrunner, Sophie Rosenmeier +1
Let be the constant such that the expected length of the Euclidean minimum spanning tree of random points in the unit square is in the limit, when goes to…
On Spheres with Points Inside
Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian
We generalize the classic definition of Delaunay triangulation and prove that for a locally finite and coarsely dense generic point set, , the -simplic…
Chromatic Topological Data Analysis
Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner +1
Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recen…
Banana Trees for the Persistence in Time Series Experimentally
Lara Ost, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner
In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tr…