RMRostik Mertz
Rostik Mertz
*This is an algorithmically generated author record based on publicly available information.
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Rostik Mertz has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Anna Schenfisch
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
1 shared publication - Brittany Terese Fasy
Montana State University
1 shared publication - Daniel Salinas
School of Computing Montana State U
1 shared publication - David L. Millman
School of Computing Montana State U
1 shared publication - Jordan Schupbach
Depart. of Mathematical Sciences Montana State U
1 shared publication - Lucia Williams
University of Montana, Missoula, USA
1 shared publication
Latest Publications
- Open Access
Reconstructing Embedded Graphs from Persistence Diagrams
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space. Recent work has shown that well-chosen (finite) sets of PDs can differentiate between geometric simplicial complexes, providing a method for representing complex shapes using a finite set of descriptors. A related inverse problem is the following: given a set of PDs (or an oracle we can query for persistence diagrams), what is underlying geometric simplicial complex? In this paper, we present an algorithm for reconstructing embedded graphs in $\mathbb{R}^d$ (plane graphs in $\mathbb{R}^2$) with $n$ vertices from $n^2 - n + d + 1$ directional (augmented) PDs. Additionally, we empirically validate the correctness and time-complexity of our algorithm in $\mathbb{R}^2$ on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.Open AccessReconstructing Embedded Graphs from Persistence Diagrams
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space. Recent work has shown that well-chosen (finite) sets of PDs can differentiate between geometric simplicial complexes, providing a method for representing complex shapes using a finite set of descriptors. A related inverse problem is the following: given a set of PDs (or an oracle we can query for persistence diagrams), what is underlying geometric simplicial complex? In this paper, we present an algorithm for reconstructing embedded graphs in $\mathbb{R}^d$ (plane graphs in $\mathbb{R}^2$) with $n$ vertices from $n^2 - n + d + 1$ directional (augmented) PDs. Additionally, we empirically validate the correctness and time-complexity of our algorithm in $\mathbb{R}^2$ on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.