H. Edelsbrunner

activity

20232026

collaborators

9 papers

cs.CG2026

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 $n$ points in $R^{2}$ to the lunar EMST f…

math.PR2025

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 $c$ be the constant such that the expected length of the Euclidean minimum spanning tree of $n$ random points in the unit square is $c n$ in the limit, when $n$ goes to…

math.CO2024

On Spheres with $k$ 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, $A \subseteq R^{d}$ , the $d$ -simplic…

cs.CG2024

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…

cs.DS2024

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…

cs.CG2024

The Euclidean MST-ratio for Bi-colored Lattices

Sebastiano Cultrera di Montesano, Ondřej Draganov, Herbert Edelsbrunner +1

Given a finite set, $A \subseteq R^{2}$ , and a subset, $B \subseteq A$ , the \emph{MST-ratio} is the combined length of the minimum spanning trees of $B$ and $A ∖ B$ …

cs.DS2023

Dynamically Maintaining the Persistent Homology of Time Series

Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, Monika Henzinger +1

We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion…

math.CO2023

Maximum Betti numbers of Čech complexes

Herbert Edelsbrunner, János Pach

The Upper Bound Theorem for convex polytopes implies that the $p$ -th Betti number of the Čech complex of any set of $N$ points in $R^{d}$ and any radius satisfies $β_{p} = O(…