Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Håvard Bakke"'
For a set $P$ of $n$ points in general position in the plane, the flip graph $F(P)$ has a vertex for each non-crossing spanning tree on $P$ and an edge between any two spanning trees that can be transformed into each other by one edge flip. The diame
Externí odkaz:
http://arxiv.org/abs/2410.23809
Recently, $p$-presentation distances for $p\in [1,\infty]$ were introduced for merge trees and multiparameter persistence modules as more sensitive variations of the respective interleaving distances ($p=\infty$). It is well-known that computing the
Externí odkaz:
http://arxiv.org/abs/2403.07200
Autor:
Bjerkevik, Håvard Bakke
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is well known to be unstable in a certain precise sense. Until now, it has not been c
Externí odkaz:
http://arxiv.org/abs/2305.15550
Autor:
Bjerkevik, Håvard Bakke
We show that reconstructing a curve in $\mathbb{R}^d$ for $d\geq 2$ from a $0.66$-sample is always possible using an algorithm similar to the classical NN-Crust algorithm. Previously, this was only known to be possible for $0.47$-samples in $\mathbb{
Externí odkaz:
http://arxiv.org/abs/2112.03656
We establish tight bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distan
Externí odkaz:
http://arxiv.org/abs/2112.00720
In the field of topological data analysis, persistence modules are used to express geometrical features of data sets. The matching distance $d_\mathcal{M}$ measures the difference between $2$-parameter persistence modules by taking the maximum bottle
Externí odkaz:
http://arxiv.org/abs/2111.10303
Motivated both by theoretical and practical considerations in topological data analysis, we generalize the $p$-Wasserstein distance on barcodes to multiparameter persistence modules. For each $p\in [1,\infty]$, we in fact introduce two such generaliz
Externí odkaz:
http://arxiv.org/abs/2106.13589
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 $1$-interleaved is NP-complete, already for bigraded, interval decomposable module
Externí odkaz:
http://arxiv.org/abs/1811.09165
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 determining the interleaving distance in several settings. We show that the in
Externí odkaz:
http://arxiv.org/abs/1712.04281
Autor:
Bjerkevik, Håvard Bakke
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant $(2n-1)$ that is
Externí odkaz:
http://arxiv.org/abs/1609.02086