2 papers
math.AT2025
Expected Complexity of Persistence Barcode Computation via Matrix Reduction
Barbara Giunti, Guillaume Houry, Michael Kerber +1
We study the algorithmic complexity of computing the persistence barcode of a randomly generated filtration. We provide a general technique to bound the expected complexity of redu…
math.AT2025
A Unified View on the Functorial Nerve Theorem and its Variations
Ulrich Bauer, Michael Kerber, Fabian Roll +1
The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often nee…