289 citations · 628 across the 35 of their papers we have counts for
6 papers · 1 filter
Keeping it sparse: Computing Persistent Homology revisited
Ulrich Bauer, Talha Bin Masood, Barbara Giunti +3
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topo…
Parameterized inapproximability of Morse matching
Ulrich Bauer, Abhishek Rathod
We study the problem of minimizing the number of critical simplices from the point of view of inapproximability and parameterized complexity. We first show inapproximability of Min…
The Morse theory of Čech and Delaunay complexes
Ulrich Bauer, Herbert Edelsbrunner
Given a finite set of points in and a radius parameter, we study the Čech, Delaunay-Čech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete…
Distributed computation of persistent homology
Ulrich Bauer, Michael Kerber, Jan Reininghaus
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation…
Measuring Distance between Reeb Graphs
Ulrich Bauer, Xiaoyin Ge, Yusu Wang
One of the prevailing ideas in geometric and topological data analysis is to provide descriptors that encode useful information about hidden objects from observed data. The Reeb gr…
Optimal topological simplification of discrete functions on surfaces
Ulrich Bauer, Carsten Lange, Max Wardetzky
We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance δ from a given input function. The result is achieved…