289 citations · 628 across the 35 of their papers we have counts for
6 papers · 1 filter
Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations
Ulrich Bauer, Fabian Roll
Motivated by computational aspects of persistent homology for Vietoris-Rips filtrations, we generalize a result of Eliyahu Rips on the contractibility of Vietoris-Rips complexes of…
Tight quasi-universality of Reeb graph distances
Ulrich Bauer, Håvard Bakke Bjerkevik, Benedikt Fluhr
We establish tight bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, th…
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 complexity of high-dimensional cuts
Ulrich Bauer, Abhishek Rathod, Meirav Zehavi
Cut problems form one of the most fundamental classes of problems in algorithmic graph theory. For instance, the minimum cut, the minimum - cut, the minimum multiway cut, and…
Structure and Interleavings of Relative Interlevel Set Cohomology
Ulrich Bauer, Magnus Bakke Botnan, Benedikt Fluhr
The relative interlevel set cohomology (RISC) is an invariant of real-valued continuous functions closely related to the Mayer--Vietoris pyramid introduced by Carlsson, de Silva, a…
Persistent homology for functionals
Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl
We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence d…