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03/13/2023
The Localized Union-of-Balls Bifiltration
We propose an extension of the classical union-of-balls filtration of pe...
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03/12/2023
Sparse Higher Order Čech Filtrations
For a finite set of balls of radius r, the k-fold cover is the space cov...
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03/10/2023
Decomposition of zero-dimensional persistence modules via rooted subsets
We study the decomposition of zero-dimensional persistence modules, view...
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11/16/2022
Keeping it sparse: Computing Persistent Homology revisited
In this work, we study several variants of matrix reduction via Gaussian...
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11/10/2022
Filtration-Domination in Bifiltered Graphs
Bifiltered graphs are a versatile tool for modelling relations between d...
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11/19/2021
Asymptotic Improvements on the Exact Matching Distance for 2-parameter Persistence
In the field of topological data analysis, persistence modules are used ...
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11/03/2021
Average complexity of matrix reduction for clique filtrations
We study the algorithmic complexity of computing persistent homology of ...
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07/22/2021
Compression for 2-Parameter Persistent Homology
Compression aims to reduce the size of an input, while maintaining its r...
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05/11/2021
Improved Approximate Rips Filtrations with Shifted Integer Lattices and Cubical Complexes
Rips complexes are important structures for analyzing topological featur...
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03/14/2021
Computing the Multicover Bifiltration
Given a finite set A⊂ℝ^d, let Cov_r,k denote the set of all points withi...
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10/29/2020
Fast Minimal Presentations of Bi-graded Persistence Modules
Multi-parameter persistent homology is a recent branch of topological da...
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12/12/2019
Efficient Approximation of the Matching Distance for 2-parameter persistence
The matching distance is a computationally tractable topological measure...
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12/06/2019
Topology-Preserving Terrain Simplification
We give necessary and sufficient criteria for elementary operations in a...
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01/25/2019
Metric Spaces with Expensive Distances
In algorithms for finite metric spaces, it is common to assume that the ...
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12/21/2018
Exact computation of the matching distance on 2-parameter persistence modules
The matching distance is a pseudometric on multi-parameter persistence m...
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12/12/2018
Improved Topological Approximations by Digitization
Čech complexes are useful simplicial complexes for computing and analyzi...
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11/22/2018
Computing the interleaving distance is NP-hard
We show that computing the interleaving distance between two multi-grade...
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09/26/2018
A Kernel for Multi-Parameter Persistent Homology
Topological data analysis and its main method, persistent homology, prov...
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06/22/2017