27 citations · 35 across the 5 of their papers we have counts for
7 papers
Computing -presentation distances is hard
Håvard Bakke Bjerkevik, Magnus Bakke Botnan
Recently, -presentation distances for were introduced for merge trees and multiparameter persistence modules as more sensitive variations of the respective int…
Stabilizing decomposition of multiparameter persistence modules
Håvard Bakke Bjerkevik
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be…
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…
Asymptotic Improvements on the Exact Matching Distance for 2-parameter Persistence
Håvard Bakke Bjerkevik, Michael Kerber
In the field of topological data analysis, persistence modules are used to express geometrical features of data sets. The matching distance measures the difference…
Computing the interleaving distance is NP-hard
Håvard Bakke Bjerkevik, Magnus Bakke Botnan, Michael Kerber
We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are -interlea…
Computational Complexity of the Interleaving Distance
Håvard Bakke Bjerkevik, Magnus Bakke Botnan
The interleaving distance is arguably the most prominent distance measure in topological data analysis. In this paper, we provide bounds on the computational complexity of determin…
Stability of higher-dimensional interval decomposable persistence modules
Håvard Bakke Bjerkevik
The algebraic stability theorem for -persistence modules is a fundamental result in topological data analysis. We present a stability theorem for -dimensional rectan…